I don't think so. As far as I understand it is accepted that neoconservativism endorses foreign intervention and democracy.

Thiel has been against these misadventures to 'reform' the Middle East and he isn't a fan of democracy.

That Leo Strauss was an influence on the neocons and Thiel doesn't imply he is a neocon. That seems like a category error. It is a common failure mode on both sides of the political divide to lump different but connected groups together.