616's Emma's school was a real boarding school for rich kid humans. She only had a small squad of Hellions, who yes, were meant to be commodities for the Hellfire Club( I mean, hello, Emma was created as a villain... even if Claremont did temper that a bit when he used her more in the NM run. She wasn't sooo evil there, even if she was basically trying to enslave humanity.).
That said, the Ultimate version also ended up being tied to the Hellfire Club if I remember correctly(Emma was dating Shinobi Shaw, who was funding the school and was also a member of a new branch of the Hellfire Club(the previous one, including Sebastian Shaw, having been destroyed by the Phoenix earlier in the run).
*I did like that part of the Millar's Ultimate run, his version of the DPS positioned the Hellfire Club in a more Freemasons/Illuminati-type role, a collection of all the most powerful businessmen/politicians who were using arcane Egyptian magic to try to control the Phoenix.
But yes, ultimately Claremont's run is the meat and bones of the franchise, and I'd love to see it adapted in film and show formats by the MCU.