edit Some incredible links/pointers for more info and a lot of solid explaining - thank you all!
Yes and no. You also see similar scenes in "We Were Soldiers" (when Col. Moore calls in the infamous "broken arrow" command over the radio) and in Forest Gump when Lt. Dan calls in the airstrike in which he loses his legs. Although these are Hollywood depictions, they both illustrate the joint effort that ground and air forces used in close quarters combat in Vietnam.
Vietnam marked a turning point in the way in which aerial warfare worked in support of ground forces. The maturation of the helicopter as a weapons and support platform allowed for:
the evacuation and movement of combat teams around the battlefield,
the relay of information to support teams, chains of command, etc.
the ability to instantaneously supply troops
which created a fluidity of battle that was rarely seen in previous wars. The result of these new battlefield developments was the evolution of an indefinite "front line," i.e. more chaotic battlefield, but it also gave a new medium of aerial support for the troops on the ground. In this war, aircraft could hover over the battlefield and maintain communications to the soldiers on the ground, and could act as a relay between the command in the rear, and other weapons assets (artillery, other aircraft, etc.) Thus, a platoon radioman now had the power to call in direct air support, and could relay accurate, up-to-date information farther distances than in previous wars. This tactic is still widely used (we see it again in Black Hawk Down) and has evolved with the invention of drones.
It wasn't just the helicopter that fit the role as a fire/support asset. In John Plaster's book SOG, The Secret Wars of Americas Commandos in Vietnam and John Burford's autobiography "LRRP Team Leader: a Memoir of Vietnam, both authors describe having a "bird dog" eye in the sky during their various patrols. These were literally special ops guys in Cessna's flying over the battlefield giving updates on artillery strikes and maintaining communication with the ground forces in a role reminiscent to modern day forward observers.
As you can imagine, air support wasn't available 100% of the time, due to hierarchical priority given to specific missions, emergency tasking, and the need to return to base to rearm and refuel.
In regards to the type of armaments at the disposal to these aircraft, it was common to load the plane up with multiple different types of ordinance so that the pilot could choose the best bomb for the job. HE (high explosive) bombs were used for general bombing, while anti-personnel "cluster bombs" and napalm were used for indiscriminate area bombing.
The Arc Light B-52s were used in this fashion starting in 1965. They were pulled off of SAC nuclear alert and were fitted with conventional ordnance and were modified in the "big belly" program to enlarge the bomb bay to carry even more bombs: ~22,000 lbs more than the unmodified aircraft. The Arc Light missions were flown with close coordination with ground forces and were used to directly interdict in tactical battles, seeing notable use in battle of Khe Sanh.
B-52s were later used in Linebacker I and II in a more strategic role; flying missions primarily over Hanoi and the Red River dike system.
Source: Factsheets, Operation Arc Light, Air force Historical Studies Office
In addition to what IrishWaterPolo said the scene in Apocalypse Now depicts a battalion assault so artillery and air assets would have been notified of the attack and been ready to provide quick response.
Generally close air support wouldn't be patrolling, it would either be dedicated to a ground unit and waiting very close by for orders, or it would be in a tactical area pool waiting to be assigned a target (see the "cab rank" system in WWII) and could take tens of minutes to get in position for an attack.
Past 1966, they'd always have a Douglas AC-47 Spooky circling over Vietnam, swooping in and providing ground fire when needed, and another on standby.
Spookies was also nicknamed "Puff the Magic Dragon", because they had three 7.62 mm mini guns, which could pour fire directed by radiomen on the ground; apparently the smoke poured out of those suckers. I vet I once spoke with told me that they were a terrifying sight.
This video shows them in action; it's too bad there isn't more footage of a Spooky from the perspective of a ground soldier.
For an excellent insight into the workings of US air power in Vietnam and Laos I would recommend giving "The Ravens" by Christopher Robbins a look. Its told from the perspective of forward air commanders, who were responsible for recon and directing airborne assaults.
Was the "Cab Rank" system still in place at the time of the Vietnam War ? Or did it evolve in something else - did it have a name ?