WARNING: This post includes comments which may make you feel negative emotionally if you are deaf or suffer from hearing disabilities.
I know some people might say it doesn't, but even to them soundtrack matters, it just does subconciously. If you don't believe me, make it concious by cutting the soundtrack out of a game completely. In a lot of the cases you will notice that this makes it far less immersive. But why limit this to soundtracks? Sound effects and other sounds are also important. TF2 for instance has no music ingame, but the noises of the weapons and the one-liners from the characters really make the game come alive and you'd miss so much of the fun with mute on or speakers off.
Even leaving the sound away can have a drastic effect, like when there's a soundtrack at all other times, but it's just snipped out in some graveyard level. It gives the game a real sense of loneliness and hollowness amongst the graves. Sounds are simply the spice of games and are part of what can make an experience have so much impact.
And I'd like to finish naming an example of an awesome soundtrack, which would be Bionic Commando (2009). Now, I can't really qualify that statement, because I'm not really good with psychology related to music, but for me swinging through the city, shooting from the sky with the game's ridiculous, over-the-top patrioatic action music did make the experience incredible for me. The title screen has this classic piano piece which makes you feel like you're floating (or swinging on a grappling hook so to speak) and there's this bit in the middle which isn't of any importance at all, but has the only piece of Heavy Metal with spoken dialogue in the game.
That's pretty rare by itself outside of Devil May Cry clones (from what I understand), but that 5 second piece of song just made me feel so in sync with the action-packed situation, yet
was in a lull so it wasn't trying too hard to be dramatic; it was just for the sake of the music (the creators probably liked that song I suppose). Whatever, the case, you can say what you like about Bionic Commando, but the music is fantastic and most definately the best I've ever heard in a video game.