I was thinking about this yesterday, actually.
Yes, it should pull flavour from the apples--what you are thinking is no different from making an apple liqueur from scratch.
Issues: You will probably also get some sugars from the apples, which may ferment in the bottle if there is any living yeast left (I doubt you would have to worry about bottle bombs, but that is for you to decide. Look at threads on bottle carbing and pasteurizing, if you want). I don't know about using everclear--it seems a bit harsh to me--but that is up to you. I do suggest adding a bit at a time until the flavour is where you want.
Dammit--now I want to make apple liqueur!
Slainte!