Such a thing seemed as if it would be completely plausible, but how widespread was it? If it did occur, how zealous were prosecutions after the war was over when such people were found?
Before the institution of a national identity system, i.e. a social security card, it seems like it would have been pretty trivial to assume a new identity by just moving further away?
During Word War I, our case for going to war wasn’t nearly as strong as in World War II. The war was in some ways “forced”. There was a lot of protest.
To avoid this during World War II, a very robust system for “Conscientious Objectors” was set-up. You wouldn’t have needed to necessarily disappear at all to avoid war. You could take a non-combat role, go to work at a CCC camp, etc. There were CO’s during WWI, but not as many. Ironically though because the case for war was much stronger there was much less resistance than in WWI.
Also during WWI, only 10% of those registered (about 25 million) for the draft were drafted, so outright evasion would have been dumb unless your number actually got called.
After WWII, Truman pardoned all draft resisters / evaders. There were 373,000, of which about 5% convicted until they were pardoned.
Sorry I couldn’t answer all of your questions, hope that sheds some light.
SOURCE: The Military Draft Handbook by James Tracy