Can cuttings be taken from "dwarf" trees and grown?

I'm asking because I recently bought a tree described as "Meyer Lemon Dwarf" from a seller on eBay. One of the tiny newly formed branches fell off because it was growing at a joint where one of the leaves would push it out the way as the sun rises. I stuck it in some water about three weeks ago and it's still alive and looks like it's gotten larger.

From what I've read, these sorts of trees are grafted onto rootstock? If the branch managed to root, and I planted it, would it have the same chance of producing fruit as the mother plant?