> are they in fact making money overall on youtube?

if they weren't, won't it make sense to drop it? So by empirical observation of the outcome, it seems like youtube produces enough value to google that it is worth the investment!

Now if you ask whether youtube is financially net-positive; ala, if youtube were to be spun off as an individual/separate entity without being owned by google, then that's another question altogether. I have doubts it is financially net-positive without the leverage that google provides in utilizing youtube's assets.