Saps are definitely edible from several trees -maple, birch, sycamore etc - see this post for details:
http://www.bushcraftuk.com/community/showthread.php?t=5623
However, I don't know of many resins that are edible - pine-tree resin used to be used as a type of chewing gum, and is apparently rich in vitamin C, but then most resins also contain things like turpentine that you probably wouldn't want to eat.
With most trees that contain resin, you'd probably be better using other parts as a foodstuff (bark from young twigs, leaves, needles, seeds etc) if they are available.