Transaction verification
Yes, your client will fully verify each block it receives. 

Your biggest issue with accepting 0-confirmation transactions is making sure an attacker can't send your node(s) a transaction that the rest of the network will discard as a double-spend. Basically you'll want to disallow direct connections to your node(s) and connect them to trusted nodes such as large miners. 

This doesn't eliminate risk but reduces it somewhat to Finney attacks and an attacker getting lucky with getting the bad transaction to you through a big miner that ends up not putting that transaction in a block before the conflicting transaction is mined.