Yes and no. There's a new set of achievements/trophies for the Hitman 1 legacy content in Hitman 2 that's exactly the same as Hitman 1. So you can do it all again if you want (or get them for the first time) lol. But nothing carries over at all, whether it's in game progress or achievements.
Perfect. Thank you very much for the explanation! Guess I'll just wait til my Hitman 2 copy comes in tomorrow before I just play the entire series. Should be a fun weekend!