I don't know if Game Genie works on Genesis 3
the 32x and Powerbase Converter don't, as the Genny 3 has no z80 processor, which also means, most games don't work period.
it is confirmed, by many. the Genesis 3 does not have the z80 chip.
1. Unable to run the MS convertor as it needs the Z80 chip which is the brain of the SMS.
2. Unable to run Game Genie, the Z80 must have played a role in the use of this for code break ins.
3. Unable to run special games such as Sega's Virtua Racing, which again uses the Z80.