Depends on whether they focused on the setting or the plot of Harry Potter, the setting I think could be expanded to fit a common MMO but the plot was all completely hinged on guess who? Harry potter. I personally think the reason Harry Potter did so well was because of the setting was a really cool wizardy world where magic was everywhere and being used as a cheap readily accessible alternate to technology and you could just go crazy.
I think a lot of MMOs could stand to move a bit away from the combat setting and could use things like the miscelaneous spells and enchantments used by the early harry potter movies (Moving stair cases, invisibility cloaks, flying brooms sticks, balls that help you remember things, candy that's made to be played with, pictures that are alive, spells to provide minor convience, that sort of thing.
The second movie/book introduced a whole 'nother set of artifact type things as well as some mythical creatures like the pheonix and basilisk which was cool, third developed the social structure of the wizarding world and how it basically manages to function (the prison, the ministry of magic, where the fuck ups wind up) the fourth showed that it was a much bigger world that spanned really everywhere with the other schools, the fifth and sixth were both just there to wrap up the plot so those wouldn't be as useful.
Classes could be based on the different classes of magic, transfiguration, charms, potions, dark arts/defence against, beastiology.
Quests would be tricky and require some innovation but you could do things like capture the flag for pvp (Done to death but I think it would be interesting if it was more like real life capture the flag where it was all about dodging away and avoiding opponents on their side and catching them on your side using things like camouflage, spells to invert peoples controls, potions to increase speed/luck/performance, enchanted animals to distract enemies and transforming oneself)
where as PVE could be like fighting dark wizards or series of small one shot adventurers.