I'm also curious, with Starfleet being somewhat military-like, if resigning is always allowed? I wonder if they could have rejected Data's resignation.
Well yeah, that was the whole point of the episode. Maddox was trying to prove that Data couldn't resign because he was merely property.
I see what you mean though. Starfleet's recruitment is quite ill-defined. We don't even know if they introduced conscription in the Dominion War. By and large, we only see Starfleet's best and brightest officers, who have chosen their careers carefully. Maybe all those redshirts scrubbing plasma manifolds on the USS Richard M. Nixon were draftees?
The nearest we get is Bones falling foul of the reserve activation clause - but by definition that suggests McCoy remained a reservist rather than resigning completely.