After replacing a 1-gang electrical box with a 3-gang box, am I allowed use the same 1-gang wallplate and drywall over the rest of the box?
No, you can't box a box in like that!

When you have a multigang box, all the innards need to be accessible without removing any building finish, as per NEC 314.29, so that the next bloke who services the thing can get at all the stuff inside.  Your choices are to either use a 3-gang to 1-gang mudring (as was linked in the comments), or to use a 3-gang cover that has blank spaces (i.e. no switch or receptacle openings) in the other gangs.