I think John Harrison is an Android.
I actually thought of that one, and felt it was reasonable to explain his strength and his ability to jump from great distances. I think that no matter if you're genetically engineered or not, that doesn't allow you to do such things with great ease. There are still limits to the human frame.
However, I don't expect the writers of this movie to really take that into effect. They're not going to care if it makes sense or not because all that really matters is if the audience at large will buy it (they probably will).
There's probably lots of reasons against him being an android though. Like being in Starfleet, not being the typical portrayal of the android who doesn't quite understand humanity, etc. I could see it being that this would be the type of secret that they want to cover up and not reveal, but at the same time it wouldn't make sense that an android could make it through Starfleet without being found out. Then again, refer to my above paragraph.