Under laboratory conditions you can regrow a whole plant from an extremely small sample, even down to an individual cell. This is very handy with potatoes for example. Potatoes are notorious for acquiring many different viruses that eventually make a clone line uneconomical or just kill the whole variety altogether. With lab work it is possible to cleanse a potato cell of the virus then propagate many new, clean plants.
So if you were to take new growth and graft the same variety of apple tree for the next million years, at some point it would no longer be viable. But how many years that would take isn't really known. On a human scale, yes, they can be considered immortal.
As long as you keep grafting healthy scions, the apple trees live forever.