Can I take it you're referring to sap rather than resin, Adderrustler?
I've never heard of anyone tapping an apple tree but see no reason why the sap can't be used in much the same ways as birch or maple, although I'd do some research first to be certain.
There may be an issue with regard to tapping the life-blood of a fruiting tree affecting yield, though. I'd be happy enough with harvesting the apples.