I would like to run an APEX script after a Pardot form or form handler is entered. Is this possible?
I don't believe that there's an easy way to do this, but there is way with fairly minimal complications...
Set up a REST service on a public Site in Salesforce so that you have an unauthenticated endpoint which accepts POSTs. Then, POST to that from the "Thank You Code" in Pardot.
It's basically an instance of this:
Where the third party is SF.