Pirates of Honesty

I hold the same opinions on the Pirates of the Caribbean movies as the Honest Trailers guys do: the first one was good, the second one was tolerable, and the third and fourth was dumb as all hell. But something I had never really thought of before this trailer is the fact that Pirates of the Caribbean may well have been the thing that caused Johnny Depp to go bonkers and make stupid, wacky movie after stupid, wacky movie. If Pirates of the Caribbean had never been made, would we still have seen Depp in the unofficial trilogy of bad Tim Burton movies that was Alice in Wonderland, Charlie and the Chocolate Factory and Dark Shadows?