What woud happen to me if I touched the aurora?
The lowest reaches of an aurora is ~100 km in the air.  Your problem won't be the ionized gas, it'll be that the air pressure is close to zero.  Also, aurora are very diffuse, with at most a few glowing molecules per square centimeter.  I'm not sure at that density that you could tell you were actually in something.

If you're in a spacesuit to survive the lack of oxygen, you might worry about the high-energy electrons that sometimes make it through to those altitudes, but fundamentally your problem is that you won't really be "touching the aurora" because you're in a space-suit and you can't really see that you're in it.