Have a positive influence on decreasing crime? Not likely. When the economy got so bad recruitment shot up through the roof and those huge signing bonuses recruiters were offering went away. Anybody who would opt for a life of crime over military service to begin with is going to find a way to weasel out of the draft and we already have enough mindless idiots and borderline sociopaths in our military thanks to declining standards. Drafting more incompetent, dishonest and lazy soldies will just put more lives in danger.
An antiwar movement would be more widespread and more vocal if there was a draft but that is exactly why it probably won't happen. Big private contracters make money off these uselss wars and that is part of the reason the US gets involved in them to begin with. War is big business and a draft would probably cost these contractors money in the long run. Since they own so many members of congress they would never let something like that happen.