Here is my situation: sound does play ingame, but it plays through my HDMI monitor speakers instead of my headphones. In addition, sound simply refuses to play within the client. I have noticed that LoL is running the winealsa.drv sound driver, while all of my other PoL games with sound running through the headphones run winepulse.drv.
Info: I'm running Linux Mint 17 64-bit, with headphones plugged into the two jacks in the back of my PC. I'm not sure what other information would be pertinent.