A very interesting question, but I would say no, as I believe a tree's sap moves rather slowly through the tree. The result of this would be that the energy being used would be higher than the energy being supplied. It is an interesting idea, but I doubt it would work.
I think I ate the lime that Jeff stuck his d*ck into.
To answer your question: Sure, why not?
I dont know
maybe
If I was hoping to source power from a lemon via copper and steel, would the power be ongoing if the lemon remained connected to the tree? Like... would it regenerate?