>>212009099
>>212009306
If Adam got the key he would just have free roam around the room, which would make Doctor Gordon's side of the game more difficult, it doesn't ruin any part of Jigsaw's plan because it doesn't really matter how the game plays out.
By Saw III they were retroactively trying to expand on this. There were behind the scenes discussions about Jigsaw's apprentice, Amanda being instructed to tie the key to the plug to guarantee Adam could eventually free himself, but in the movie she just throws the key in the bathtub without caring. Jigsaw giving her specific instructions on what to do with the key never made it in to the movie, so whether or not that's canon is up to the viewer.