On an individual level, yes.

On a squad, platoon, company or battalion level, no.

The Americans were the only nation to have enough industrial power to equip every soldier with a semi-automatic rifle during world war 2. But the Americans also equipped their troops with far, far fewer machine guns and sub-machineguns than other nations, especially the Germans.

During ww2, there were basically three schools on infantry squad firepower. One of the main duties of squad firepower was supression - fire to make the enemy keep his head down and not fire back, so that your own troops could advance.

During ww1, machine guns had been belt-fed and watercooled (thus the big cylinder-shaped water jackets over the barrels), which allowed them to fire continously for a very long time compared to aircooled weapons. They were also mounted on heavy tripods - these allowed to weapon to be fixed at a horisontal level - which allowed the crew to cover specific areas of the battlefield with machine-gun fire. The British and the Canadians developed tactics where machine-gun units would fire indirectly and planned supressing fire over long distances to cover advances with these machine guns. These weapons were very heavy and very hard to bring with you in an advance, which was a big liability.

The light machine gun school, pioneered by the French and developed by the British - adherents included most of Europe, including countries such as Britain, France, Czechoslovakia, Romania, Sweden, USSR, Belgium, Italy and many others. These countries equipped their infantry squad with bolt-action rifles and a magazine-fed light machine gun on bipod with a quickly interchangable barrel. The intention was to have a weapon that was capable of the supressing fire heavy machine guns (mounted on tripods) were but quick to set up and light enough to not hinder advancing troops. Nations of this school retained heavy machine guns in specialised units, often at as a machine-gun company attached to a regiment of infantry to provide the ww1 type supressing planned fire.

The second school was that of the general purpose machine gun. Instead of using magazine-fed light machine guns they made the ww1 machine gun lighter - adding an advanced air cooling (and thus removing the heavy water cooling), rapidly interchangable barrel, bipod (but the same gun could be mounted on a tripod if needed) and pistol grip. Germany was the only real adherent of this school before ww2 and their MG 34 and MG 42 are primary examples of this. These were belt-fed weapons and heavy compared to the light machine guns used by other nations (Bren Mk III - 8,68kg empty, MG 34 - 12,1kg empty).

The third school was the rifle firepower school - while the British had been adherents to this school before ww1, the only adherent before ww2 was the Americans. The Americans believed that if each soldier was equipped with a semi-automatic rifle, they would be able to provide their own covering fire. The American BAR did not have a pistol grip and did not have an advanced air cooling system nor did it have an interchangable barrel, which made it unable to provide supressing fire. It can be interesting to note that other nations that used the BAR (Sweden, Belgium and Poland) as their primary light machine gun made it with a more advanced air cooling system, pistol grip and rapidly interchangable barrel while the US did not.

This American doctrine left a US battalion 1943 with only 8 machine guns (plus 27 BARs, if you want to count them despite them being uncapable of sustained fire) while a German 1943 battalion had 44 machine guns and a British battalion had 63 light machine guns.

To make matters worse, the Americans shunned the sub-machine gun - while other nations equipped their NCOs and eventually both squad leader and squad leader assistant with an sub-machine gun, the American army equipped them either with an M1 Garand or the ligher M1 Carbine (which also fired semi-automatically). Sub-machine guns were used for rear area troops in the American army, except for among the paratroopers (which also used M1919A6 bipod-mounted belt-fed general purpose machine guns). The Soviets went so far that they equipped a sub-machine gun company in every infantry regiment with only light machine guns and sub-machine guns.

The bottom line? During the war, the German experience was that infantrymen did not need a full power rifle round - combat distances were usually 50-300 meters and not further than that. Catridges capable of killing at 1 200 meters (as standard ww2 catridges were) were not needed. The sub-machine gun, firing pistol rounds, had a range of about 30-50 meters, which also made it less than optimal, although the firepower was excellent. Thus they started to merge the rifle and the sub-machine gun into the assault rifle, based around a shortened rifle cartridge, which is what became the MP 43/StG 44.

After the war, the American school lived on for a while with the M14 service rifle, but in the end, the German school took over. Today troops are equipped with assault rifles and general purpose machine guns (belt-fed with bipod, aircooled with advanced air cooling systems and with a rapidly interchangable barrel).

To asnwer your questions - the doctrine that gave the US troops the M1 Garand rifle also gave them no sub-machine guns and very few machine guns (and all of them heavy tripod-mounted) and an inadequate light machine gun. While the M1 Garand was an excellent rifle, experience was that it could not compensate for the lack of firepower of the American infantry. It was instead the absolutely superb American artillery (and how superbly it was integrated with the infantry), including mortars, that made the American infantry division the fearsome and effective formation it was.

I'm without a campus library at the moment so providing good sources will be difficult, but here's the information as I understand it regardless.

the average US rifleman using the semi-automatic M1 Garand must have had a significant rate of fire advantage compared to his German/Japanese counterparts.

They did, not just because of their rifles but also because they were rarely low on ammunition. While it was rare for small arms cartridges to be in short supply for anyone, it was particularly rare for the United States.

To what extent was this an advantage?

Not as much as you would probably expect, particularly compared to the Germans, but also in general. I'll use the Germans as an example since they are particularly vivid.

While the German army did see pretty serious upgrades in the firepower of basic riflemen throughout the war (going from a shortened version of the G98 bolt actions they had originally used in the First World War to semi-automatic gas-powered designs like the G43 and even to the world's first automatic/semi-automatic assault rifles in the MP44), they nonetheless organized their squads as mainly supporting elements for their machine-guns. They did this based on the theory that not only would the machine-gun put out dramatically more firepower than the rest of the squad (even if the rest of the squad was armed with then-modern rapid-firing rifles), but that the machine-gun would prove to be the critical element in the opening salvo of contact with opposing infantry elements before they scattered to cover and concealment.

It turns out that the Germans were correct on both counts. Fired in controlled bursts, German squad level machine-guns were easily capable of 300 or 400 accurate rounds per minute, making them equivalent alone to almost a dozen American GIs armed with Garands. Similarly, many studies have been published indicating the efficacy of striking from ambush against unaware targets using overwhelming, accurate, sustained firepower (one that comes to mind is US Army Ballistics Research Lab report no. 798, later published under the name Data on W. W. II tank engagements involving the U.S. Third and Fourth Armored divisions as a small book, although obviously this was one published for tanks). Reportedly the German Army Handbook of 1940 contains information to this effect as well, although I don't have a copy. Again, sorry for the somewhat poor sourcing on this if you want independent verification.

Other countries, seeing the same importance of these factors, also tended to - wherever possible - concentrate their firepower around their heavier weapons. However, unlike the German army, many other contemporaneous armies lacked numerous, light, and effective machine-guns to employ at the squad level, instead relying on older or heavier models that often required a crew to operate and worked best from emplaced positions - these factors made them unsuited for squad level attachment. To use the US as an example, they often had their machine-guns attached at the platoon or even company level and tried to bridge the firepower gap by employing the Browning Automatic Rifle. Other nations with similar problems also developed very light machine-guns or automatic rifles, like the British Bren Gun or Japanese Type 96, for the same reason. Militaries today almost exclusively organize their squads around integrated automatic weapons like light machine-guns as a result of the proven efficacy of this doctrine.

On the whole, therefore, most armies of the period relied on getting most of their firepower from their automatic weapons and not from their riflemen. While American riflemen did therefore enjoy a significant firepower advantage over the riflemen of competing nations (on the order of around 4 or 5:1, generally, given the Garand's effective rate of aimed fire), when taken in the context of squad, platoon, or company level engagements - often with other supporting elements like artillery or vehicles - this advantage can probably be considered somewhat marginal.

Did accuracy suffer compared to the bolt-action counterparts?

Not so you'd notice as a typical rifleman. Most infantry combat takes place at pretty close ranges in places like Europe or tropical islands in the Pacific. Sniper variants of semi-automatic rifles from WW2 also existed (and continue to exist today, albeit not with WW2 rifles anymore obviously), which seems to indicate even for precision specialists there sometimes existed an acceptable trade-off between firepower and accuracy.

I watched a program on the Military Channel a while back that claimed how sometimes the Garand's cartridge put the soldiers in danger because the enemy became familiar with the empty discharge noise it made when the cartridge was ejected. Any truth to this?

Here is a previous thread on the matter

Related: What do we know of American soldiers "bump firing" their Garands in urban engagements? I can't find much (after an admittedly short search), but someone here may have information at hand. Bump-firing as it has been explained to me, is when a soldier would stick a finger through the trigger guard and their belt loop and use the Garand's recoil to fake automatic fire the weapon. Of course, this would never have been helpful in a long range engagement, but for clearing a room it could have value (even if the soldier wound up with a broken finger as a result).