P2Pool deposits earnings directly to your wallet address, so yes, it needs to be open. This is assuming of course that you only have one miner running, if you have more than one, then all you need to do is put your wallet address you want the coins to be sent to into the miner configuration, you don't need more than one wallet open at a time.
Sorry maybe I was being unclear. I have 3 computers I'm not using in the house...so if I ran cgminer on each do I need also need to have my litecoin wallet on each computer?
Thank you!
no. just install cgminer and mine away.