Quick Answer: FALSE.
Long Answer: See Below.
With a GameShark or the BrainBoy/MonsterBrain, they only edit the RAM. Therefore, if your Pokémon does not physically evolve by Moon Stone (Clefairy, Nidorina, etc.), it isn't possible.
The Game Genie may be only a part answer. It is basically special instructions that when you encounter something in the ROM, you replace it with what the Game Genie code has. Problem is that you need one code per evolution (one for Bulbasaur to Ivysaur, one for Ivysaur to Venusaur, etc), AND furthermore, THERE ARE SOME POKÉMON WHO DON'T EVOLVE! Making a non-evolving Pokémon evolve does not exist in the game, so either the game is hard-coded into not letting it happen or you will crash the game.