I think it can give a different kind of appreciation.
I love music; my entire life is soundtracked. I also can't play an instrument, but I do know the basic theory behind music and that sort of thing. I certainly appreciate music on several levels, and I don't think that playing an instrument offers "more" appreciation for music, so much as different.
I have a friend who lives and breathes music. He plays basically any instrument you can put in front of him, he writes music, performs music, and he definitely appreciates it. I wouldn't say "more", but he appreciates it on a different level than I do. He appreciates music as a listener and also as a musician. It's a different approach.