Yes, I've done similar.
I think PRS and PPL do a combined license for short runs (i.e. less than 100 copies) I think mine was about 20 quid.
However, no such deal exists for the record companies. I had to contact EMI but they were great... not only did they only charge £1, but additionally, they paid the pound!
But mine was a "this is what we done" that was to show sponsors / donators that their help had really gone to children that needed it, so for a company vid the details may differ.