Actually most modern ATC-systems do separate different sectors by levels also so no, in which case aircrafts on ground with transponders on would not appear for the approach controller. Transponder off during taxi is a very old fashioned way of doing this. Most of todays bigger airports require transponder on on the ground.
Have never been asked or ever heard of anyone being asked to turn transponder off once off the runway or during taxi, however heard of many cases where aircrafts have been asked to turn it ON during taxi.