Heck yeah, go for it. Cut out the best part of the stave at least as tall as your eyebrow if you can get it and make a flatbow with a small handle, parallel sides out to 2/3 the limb, and with or without a tiny reflex or flipped tips.
I have never used privet, but similar looking plum, mulberry, elm, serviceberry, chokecherry, and hawthorn staves have netted me decent bows, some pretty stout, and some that had to settle for 38 lb depending on the wood and how things went.