That GS rear derailleur will work fine with a 28 tooth rear cog, and probably coild be made to work with a 30 tooth cog. A really talented person might be able to make it workable with a 32, but would be very dependent on bike, crank, rear dropout, etc.

On the other hand, any 7-8-9 speed Shimano Deore RD will easily hamdle a 32, and probably would do a 34 (at least it has done so on 4 or 5 bikes in my experience). So I'd go the easy/proven route.