Beth being Suicidal

So i don't know if anyone's ever thought of this before but if Beth actually did kill herself in season 2 she would have been a walker right?

So the big secret would have came out then if they left her locked in the room she killed herself and went back to find her a walker

That was her biggest fear was turning into a walker but there was nothing she could do to prevent that even if she took herself out because bitten or not you were going to turn

So my question is if that were to have happened do you think Rick would have confessed to have been knowing the whole time or do you think that he wouldn't tell anyone he knew and acted clueless like everyone else

Because we know he doesn't actually believe it until the season 2 finale whenever Shane dies and he comes back almost instantly as a walker