There's different kinds of DC.

If you DC via in-game error or server error of some kind, your character is booted from the game world and you can log back in soon.

If you DC because your modem died, or your router died, or you unplugged your ethernet cable, or you force quit the FF14 application, then your character persists in the game world for 10 minutes and you can't log back in until the server boots your character out of the game world after those 10 minutes are up.