It's possible (here's a real knife in a skull and here is a practical illustration from a sword manual showing a sword through head:

but that's a surprising way to strike, both for the chosen target, and especially for the angle (downwards from above, with both men standing and the attacker being shorter). It seems like the clear out-of-universe reason for it is dramatic visual effect. It's certainly possible to go through a skull with such a sword, particularly if your opponent is basically unmoving with his back to you. But it could also glance off the skull and slide to one side. Stab through the neck might have been safer. A swing would be even surer if it hit, but would make more noise and take slightly longer, giving some chance the target might flinch or duck. Also, if there are any other foes around, Jon's sword was stuck in the head, and might take a bit to pull it out.
We don't see exactly how Jon did it, or know why in-universe. (I like to think he was going for the neck but tripped slightly and so ended up in that weird position, but that's just my sense of humor.)
What does seem to be strange in the TV version compared to the books, is the frequent neglect of helmet use. Swords are often devastating... when they aren't striking metal armor. Heavy metal armor tends to be good protection against real swords, though.
realismtag welcoming questions like this – user56reinstatemonica8 Oct 12 '15 at 21:05