Warbows are a particular interest of mine. Many were found on the Mary Rose, despite the fact that this was some time after the great days of the longbow. These are the only actual warbows we have from the period.
Excellent article on the subject.
http://www.archers-review.com/magazine-articles/june-2010-longbows-of-the-mary-rose
I would think, given the state of firearms technology in the time of Henry VIII, that warbows would be far more effective for ship to ship close combat than the muskets of the day.