Depends on what was used for the screen protector to adhere to the screen.
I have used screen protectors on all my iPads (and most of my iPhones up to the 5-series) and never encountered any issue. Having said that, once a screen protector is on, I have never removed it unless to put another one straight back on.
Also, I use the plastic-type screen protectors which use some kind of electrostatic or some other magic airy-fairy stuff to stick to the screen and the screen protectors do come off pretty easily without any residue, thus leaving me to believe that the coating (oleophobic or anti-reflective) has *not* come off the screen.
Have not used glass or other hard screen protectors which might need stronger "glues" thus I cannot comment on those.
I used my Air 2 for a few days before I put on a Tech Armor screen protector (was on sale a few days ago for about $7. It is one of those firm plastic kinds that use static and not adhesive to stick to the screen.
While I have some piece of mind, ironically the screen protector put a highly reflective surface back onto the Air 2.
Note: Just in case if someone say this is off topic, the oleophobic coating should be the topmost layer... by common sense.
After I had applied and taken off tempered glass screen protectors several times on my iPad Air 2, I once made several drops of baby oil onto the front glass to test the oil repelling capacity, and it still worked perfectly. I'm not saying that the adhesive layer of the screen protector would never wear the coatings of the screen, but I would say normally it won't "peel off completely".