To be honest, I didn't find it sick, although you haven't posted the context in which you found the link. To me, it just sounds like a group of terrible singers singing a Band Aid song. If, however, they were releasing their version as a 'novelty record' and not giving the proceeds to the Band Aid charity, then yes, that would be a bit off.
However, if it's just a bit of fun that's never going to see the pop chart, then I don't see what the problem is. It's hardly taking the food out of the mouths of starving children.
And I hate to tell you, but 'Do They Know It's Christmas' is a terrible song anyway, and the only reason people buy it is
because it's for charity. I know I'm making a sweeping generalisation, but I have not met one person who has bought it
and listened to it.
Anyway, I'm digressing. Personally, I find the link amusing, if not a little painful to listen to. It's not offensive to me at all. Sorry if that wasn't the reaction you were looking for, although I did wonder for a minute if you were pulling our legs by appearing so outraged at such a superficial thing as a 'joke' recording of a song.