Yes, you can do that. In Nevada that's cheating and in New Jersey it isn't (but if they see you doing it they can make your life very difficult), but at that point you're operating outside the norms of the game so I didn't count it.
Seems like over the years the way they've dealt with card counters is by tweaking the game, though. They've added decks, they shuffle sooner, they shuffle when you increase your bet or when a new player sits down and plays for nontrivial amounts, and lately with continuous shuffling machines.