Not really. Two reasons.
(1) It's a popular myth that full moon is the best time to photograph it. But it looks much better when it isn't full, because the mountains and craters along the terminator have really contrasty low-angle light on them. At full moon it's all a bit dull and flat. The best time for photography is about now, when there's an attractive crescent visible after sunset. (And you don't need a dark-sky location, because the moon is so bright.)
(2) A full moon negates the benefits of having dark skies, and makes it harder to get good photos of stars, milky way, etc.