As an example, if Americans captured German military rations, would they cook and eat them?
If a German soldier came across an American Thompson machine gun and a few crates of ammo, would he pick it up and use it?
Enemy rations would certainly be eaten. If food was short then anything that could be scavenged or captured helped; even where standard rations could be regularly supplied they tended not be varied and grew monotonous, making captured items appreciated for their variety. In addition to small quantities of food captured on an ad-hoc basis, large quantities taken from supply dumps could be integrated into official distribution channels if necessary. In September 1944 for example, with Allied logistics in Europe under considerable strain: "Both [First and Third US] armies staved off total depletion of their reserves only by using captured supplies. In a few cases German rations were a welcome relief from the monotony of the operational rations on which the combat forces had subsisted during most of the pursuit." (Logistical Support of the Armies: September 1944 - May 1945, Roland G. Ruppenthal) As the logistical situation improved so the reserves of food steadily built up, though in the final weeks large numbers of prisoners had to be fed who were mostly provided with captured stocks.
In the Pacific, on Guadalcanal in 1942: "In the latter part of September (...) supplies on Guadalcanal had been so scarce that had it not been for the captured Japanese rations and gasoline, the lot of the troops would have been "extremely desperate."" (United States Army in World War II: The War in the Pacific) The Intelligence Bulletin, a publication on enemy tactics and equipment, carried an article in October 1944 "[Captured Japanese rations may be eaten] (http://www.lonesentry.com/articles/japanese-rations/)" detailing common foods found in Japanese ration packs with illustrations and instructions on preparation, and ends: "The Quartermaster General advises the fullest use of captured enemy food, after it has been inspected and approved by competent personnel. (...) The principal thought in using captured foods should be to ease our own supply problem to some extent. To waste supplies—even enemy supplies—is foolhardy."