I'm inclined to it being rather OOC. As far as we know, Harry being able to sing hasn't been mentioned in the books at all. I think if he would have any such talent, JK would have told us so. The books are from his point of view and there have been no references to him being prone to singing or having any musical taste. There is always the possibility of him having *some* musical talent, but I don't think singing is one of them. Playing the piano might be an option you'd like to consider. However, if it isn't necessary to your story, it's wise to stay away from this subject.
Good luck and I hope that answered your question!
(I love you too Ashley )