Yes, you can block advertisements from appearing on Youtube channels.
This only works on videos that the user has uploaded. I looked at the channel in the original post, which has approximately 70 nice music videos, all were uploaded. In the Youtube settings panel for the channel, you have the option of disabling ads on all videos that you uploaded. It can't be done on an individual basis; it is all or nothing. This option has been there for awhile, even prior to the changes to Youtube that Google did recently, but it was in a different (easier to find, for me) place before. It may have been directly in AdSense or AdWords, I don't recall now.
Note that it is NOT possible to disable advertising for videos that you did not upload though, not as far as I can tell.