The TL;DR here is: It was cause for great optimism for the Austrians, but the realities of the existing situation were so terrible that the optimism was washed away within a month. I believe the Germans were able to make out slightly better, redeploying forces to the west and using captured Baltic territory for food and resources.
The peace with Russia did give a lot of hope to the Central Powers... for a short period of time. Really, it started to fall apart almost immediately. Among the "realistic" counterfactual scenarios of the war (alternate histories) where a Central Powers victory is a projectable outcome, the scenario of "Germany waits just a little longer to proceed with unrestricted submarine warfare" is pretty much the only late war offering.
The immediate problem was the while Germany hoped Russia leaving the war would bring victory (German command expected to be able to redeploy 25 divisions to the western front, for instance, in addition to the food and other resources they would gain access to), Austria just needed the war to end on basically any terms. The starvation problem was worse in Austria than it was in Germany, due to a combination of factors:
agricultural issues: decline in soil fertility, bad weather, lack of draft animals and human laborers to work the land properly, government interference/bungling) which Germany also experienced
Strategic geographic flaws in the Austro-Hungarian lands: a significant portion of Austrian productive land was on the north and east of the Carpathian range, was never defensible from the start, and was ruined by battle and the local population dispersed by the summer of 1915.
A general breakdown in national logistics: A lack of coal supply to power trains and a lack of metals with which to maintain the rolling stock and tracks meant that there were difficulties in transporting foodstuffs from Hungary (the unspoiled breadbasket, after Galicia was occupied by the Russians then ruined by battle) to the rest of the Empire.
So Vienna was wretchedly desperate for any peace that was at least status quo, and this caused them to make some bad decisions. Much like the USA 100 years later in the Middle East, when a rag tag group of people making dubious claims of national leadership of Ukraine offered to make a deal with Austria the Vienna diplomats couldn't control themselves. In exchange for the promise of one million metric tons of grain by the end of July, Austria not only promised to restructure the internal politics of Galicia by splitting the Ruthene dominated Eastern Galicia from the Polish dominated Western Galicia but also agreed to givethe territory of Chelm/Kholm/Cholm/Kulm (depending on how you want to romanize the non Roman spelling, although the last one is German) which is today in eastern Poland and was also at that time considered a Polish domain by the Poles.
What Vienna got from the deal was suffering. The rag tag band of miscreants turned out to have no national authority and were deposed by the Germans in favor or a more effective leader. Ukraine shipped only 113,000 tons of grain total to all Central Powers nations (total for the war), of which Austria-Hungary received maybe 60,000 tons, a mere rounding error of the million tons they believed they needed by August. And for this pittance, Vienna’s bungling began unraveling the Empire. The Austrians tried to hide the terms of the treaty (it was never ratified by the Austrians for this purpose), but Germany published the terms of the treaty… because of course they did. The bartering of Polish lands was a vile betrayal against the Habsburg Poles, who had generally been among the most committed ethnic groups to supporting the Emperor. The Poles believed that Kholm was theirs (with fair reason), abut also believed that Eastern Galicia was theirs by right as well (with less reason, because while the Poles made up a “management” caste in the region the great majority of the people were Ruthenes(Ukrainians)). Polish officials across the Empire protested and resigned. The Polish legions deserted Austrian service and crossed into Russian territories. Civilians protested and defaced Habsburg government offices. Protests sometimes turned violent, either against Habsburg police or civil authorities, or against Jewish communities. The Jews were seen as the most loyal Habsburg supporters, and also accused of hoarding food, manipulating prices to cheat people (standard anti-semetic trope stuff). In comparison with Woodrow Wilson’s 14 points announced the month before, Habsburg actions couldn’t have looked more ill considered.
Militarily, the peace with Russia also proved to be a false hope. Austria was suffering from severe manpower limitations both in civil and in military life. The Habsburg army had been broken by Conrad in the opening Galician campaign, and the replacement drafts of third rate reserves and prime aged men had been shattered and ground into dust by Conrad in the Carpathian campaigns in the winter of 1914 and spring of 1915. From March 1915 forward you can never consider the Austrian army anything more than a militia filled with the old and the untrained. This helps explain the battle performances immensely. By 1918, even the supply of the old and the untrained was running low and industrial demands competed for the men. Schindler states that Austria had called 70% of healthy men aged 16-60. Coal, iron, and food were just as important to the nation as filling the trenches. Desertion was also endemic by the end of 1917, and the soldiers hardly got more food than civilians. The April 1918 ration of flour for a front line soldier was 283 grams (~6/10 of a pound), and there was almost no meat to be had. A rear area soldier received about 2/3 as much flour. The standard civilian bread ration was 165 grams daily.
The Austrians had made steps to improve the army. Reorganizations, rearmaments, new training for officers were all moving things in the right direction but they just didn’t have enough men (or food, or munitions). Peace with Russia opened the door to returning captured Habsburg soldiers. Watson says this was 2.1 million men, Schindler says that the Austrians had only lost 1.6 million to capture (and many of those died in Russian captivity) and that 500,000 would be returned to service by mid 1918 but regardless this was substantial in a time when Austria could only supply 100,000 new soldiers a month to the army. However, these were over a million people to feed and further Austrians were terrified they might by infected with Bolshevism. The Austrians quarantined returning prisoners for weeks, supplying them with meager food and clothing while restarting their military training, while they tried to weed out unreliable elements. Eventually, most of the freed soldiers were given back pay (of dubious value) four weeks of leave to visit families, where of course they saw the level of starvation of suffering the civilian population was enduring. Some of the soldiers, however, received neither back pay nor leave time, though Schindler attributes this to shoddy administration not malice. After this the army tried to send the soldiers back to the front. Shockingly, many didn’t want to go back! Several mutinies erupted as a result, morale continued to plummet, and the upswelling of military capability that had been hoped for never really materialized. Perhaps if there had been food and ammo to support such a thing the outcome could have been different. The Austrian army was a terminal patient at this point, and the Austrians threw away what little strength in men and material they had left at the Second Battle of the Piave River, although it took the Italians months to realize this.
Sources (and good reading on the subject:
Ring of Steel by Alexander Watson
A Hopeless Struggle by John Schindler (phd dissertation, available for free in PDF on web if you search)
Splintered Empires by Prit Buttar (this is actually book 4 of a chronological series which is very well done, but this is the book that covers the time period in question)