Not exactly. You still level up by getting more stat points in your main stats (Muscle for Seal Clubbers and Turtle Tamers, Mysticality for Pastamancers and Saucerors, and Moxie for Disco Bandits and Accordian Thieves) by fighting and completing quests and munching and drinking stat-boosting items (although it is quite hard on your spleen).
Acsension is what happens after you beat the Naughty Sorceress up and free the King. After this, the game is pretty much beaten, but you have the option to ascend. In doing so, you end up in Valhalla with infinite turns, and there is pretty much nothing to do. So instead of staying there, you reincarnate yourself, picking a new class, starting at lvl 1, and all your stuff stays at Hangk's Ancestral Storage till you can get it out. You are now an ascended character. You have the option after that of choosing hardcore mode (where noone helps you and you can't take stuff out of your storage or buy stuff from other players) and a path. There are 3 paths, Teetolar (can not drink anything), Boozefatarian (cannot eat anything), or Oxygenarion (cannot eat or drink anything).
I choose Oxygenarion Hardcore cuz I am a badass player who doesn't need anybody. I've also made a solo clan and bought all the stuff for it. I'm on my 2nd hardcore oxy run. It's a lot of fun, especially since when you complete oxygenarion paths, you get some premium canned air and plexiglass(tm) items that are better than anything out there. You can't use them on the next hardcore path, but when you finish, you're better than anyone else out there.
Yay.
Reginald Slaughterington VII of Clan MacFancypants