If not being able to monetise is an issue then you may need to take it down; I've got quite a few (I was aware of the copyright) where I've just accepted the claim and the video is allowed to stay - helpful in music-based games!
If you're putting up videos with claimed music, it won't really go against your channel, as such (I have about seven videos online and viewable but still claimed); but as mentioned previously, some videos aren't allowed to be played in certain territories, even if you accept the copyright claim.
In this current version of YouTube, they tend to claim copyrighted-music immediately and allow you to still show it, although you don't make anything from it.