Depends on what they get drafted for and how fed up they are with conditions apart from that. i honestly don't think the US would survive something like the draft during the Vietnam war again, but lots of governments get away with drafting people for non-fighting positions, historically including most liberal democracies. fairly sure that any newly instantiated draft would be gender neutral, though. the constant discussion conservatives have about that in my home country always emphasizes that point, that they'll draft everybody (read: everybody younger than them). such discussions also usually center around drafting people for all kinds of services from military to nursing jobs to disaster relief. once you re-normalize that people have to go through a period of forced labor while they're young, why stop at military stuff? There's plenty of labor shortages in other areas.

i'm not saying this to defend the dude side here, btw. i think people who make the "b-but men may get drafted" argument as supposed evidence for an imagined "female privilege" are reactionary idiots and also engage in a pointless, individualistic act of bullshitting themselves to avoid facing the entirity of patriarchal opression that damages men, women and nonbinary people alike, but still very obviously has men at the top of the hierarchy and hands out the most privileges to men as a social group. arguing that some commonly not-marginalized group has it worse than anybody else is also a type of chauvinist liberalism and can be disregarded entirely, just to make this clear. i simply made my point because the US military complained just this week that they do not have enough recruits.