You can seal off a vent anywhere: the basic goal is to have zero air leakage. So to answer your question, yes it's possible to seal a vent below a subfloor.
If you don't seal it up properly though, you'll be blowing conditioned air into the space under your floor, which is a big waste of energy and will do basically nothing.
It's better to cap off closer to the blower unit, mainly to minimize the amount of air leakage along the run. The challenge is of course finding out which runs go where, and ensuring that you aren't blocking off a vent that feeds another area as well. It's pretty common to see 5 or 6" round duct used to feed each individual vent, and larger square duct as the main runs. If you can see the round duct for the room right by the furnace, there's a good chance it's only feeding that vent.
You can get round and square ("blind") end caps of varying sizes:
If you're pulling up the subfloor anyway, I'd take the boot right off and just put a cap on the line (as far back as possible to get to). Seal all seams around the cap (and anywhere else you can see that isn't sealed) with foil tape or mastic.
If you can't remove the boot (the part that comes up through the subfloor), the next best thing would be to seal it by placing a blind end cap over the opening and sealing it up. This would basically be butted up against the new floor. If there is minimal or no air leakage through the boot, it shouldn't really heat up much, but if air is allowed to move through the vent, you'll end up with a warm or cold spot on the floor, which may be weird.