Yeah, I think this is one of those things where, from the other side of the Vietnam War, that’s what we think of when we think of the draft—young men desperately hoping their number wouldn’t be called, trying to dodge, and so on. But that whole connotation was specific to that war; it just wasn’t the same in World War II.
I think the fandom’s notion that Bucky being drafted somehow makes his military service less distinguished (and therefore, being Steve’s friend and a Good Guy, he must have volunteered) is very much informed by the post-Vietnam anti-conscription sentiment in the US.
Really, it doesn’t matter whether Bucky was initially drafted or not; he volunteered to join the Howling Commandos when he could have requested reassignment to a non-combat position due to his ex-POW status, so his willingness to serve his country (and Steve) is certainly not in question!