Can you play CO-OP on downloaded/pirated PC games?

My friend downloads a lot of single player pc games but he has never tried to play co-op. I was wondering if we both downloaded a game, for example left for dead, portal 2 or anything like could we play co-op together on different PCs. Or if I bought a legit copy of for example left for dead could I play co-op with someone who had torrented it? I don't want to do this I have bought all my games legally and i have a birthday coming up soon so I don't need to pirate anything I was just wondering.