When I had just a flat piece of metal sandwiching a regular gasket onto the bottom of my manifold, it took it about two years for the gasket to fail and turn into a fun exhaust leak whenever I accelerated on an on-ramp. Yours might be rusted in place enough to last that long with only one stud holding it in, or it might not.
I'd personally spend an afternoon with a propane torch and penetrating oil, going at that flange from above with a good-sized hammer and a brass drift. Manifolds are a pain to take off, and it's even worse trying to get the broken-off stud loose with the thing on the side of your engine (I had to do that for my main exhaust downpipe studs...survivable, but a PITA), so I'd say do your diligence this one time so you don't make a more annoying job for yourself later.
If you wanted to just buy a proper plug/gasket/new studs, you could probably just gently hacksaw through the pipe bit in the center so that flange can come off easily, then chisel/pry etc. the stub loose more easily, then deal with the broken stud at your leisure.
