What does points score do in Hitman Absolution

Yes, you can.

According to PS3Trophies.org trophy guide & roadmap, completing levels on Hard through level select is enough, see the description for the Absolution trophy (emphasis mine):

Note: If you didn't do your first playthrough on this difficulty, you can get the trophy via new story or level select.

Most of the time, Agent 47 loses the face coverings, so you end up with a bald guy wearing safety goggles, and thus he's still spotted by members of the same class of disguise (maintenance worker/plumber/policeman etc).

There is at least one noticable exception I've noticed, later in the game when you are assassinating Dexter's lady-friend, there are two or three bodyguards wearing full balaclavas. If you disguise as one of these guys, you can walk around almost the entire house without being spotted, as 47 puts on the balaclava. But this is mostly to do with the fact that you're a different "class" to most of the guards in the house, as other guards who are wearing the full-face masks are somehow miraculously able to tell that you're not one of them, even though you're not showing any skin.