I don't want to support troll hardfork attempts like Classic, should banning every time I connect to Classic nodes help Core in some way?
No, until the network is forked classic nodes behave very similar to core nodes. After the fork they will most likely get banned as soon as they try to relay blocks over 1 MB to you (someone that actually read the code please correct me if needed).
What would happen if everyone running Core banned Classic nodes from connecting to them? I just don't want those leeches anywhere near me.
If everyone would refuse connections from nodes with a certain subserv, they would form a separate network. This could easily be mitigated by changing the subver though.