Can a crown cap be so attached to the tooth that it would be pulling the tooth slowly? Or am I imagining this?

Porcelain crown, does not pull your teeth, it is there to protect the integrity of the tooth. If you feel any type of puling or movement, there is possibility of bite interference with your opposing tooth, have it checked with an expert dentist. If you do have a zerconia crown or emax they hardly wear down, but the tooth with the crown can move . Also if there is any lack of bone movement of tooth and crown is possible.

Hello Yes, of course the wisdom tooth can pushing your teeth so the best option for you is get an extraction.

Hi:Crown pulling the tooth up is not a normal occurrence unless the crown is attached to a post.Best,Dr. Maddahi

A crown is cemented to the tooth. It will not pull on the tooth. If you feel like the tooth with the crown is moving, it isn't the crown that's causing that.