Only send connections to server2 if connection limit reached on server1

Yes, I believe you could use priority activation for this as when a pool member reaches its connection limit it is "unavailable" (will have a yellow triangle) and means the next priority could can be activated if it was the only member in the higher priority group.

One quick question, if you are trying to tune for caching content have you looked at using the caching built into LTM, Web Acceleration profiles? Could have your servers some work.

https://support.f5.com/kb/en-us/solutions/public/14000/900/sol14903.html