I wouldn't necessarily say a clean story break would be required, so much as I'd say it would be optimal if they really wanted to pursue a quality MMO.
They could always do something similar to what they did with the co-op in 3 - have it set up to where you're just a soldier/biotic/Geth/whathaveyou whose story takes place against the background of the events of the series as we know, but in other places; it'd probably have to be a smaller MMO though, and probably could only reuse a handful of the locales from the series, if that. A clean break - i.e. set 100, 200, however many years after the "canonical" ending to 3 (because they'd pretty much have to decide upon one as canon, if they wanted to pursue this idea) would allow for a much more open-ended structure.
Then again, they might make a MMO set in the last time when the Reapers came, where you could play as a Promethean or one of another set of races that were alive at that time. That might be a fascinating story, especially given the specter of ultimate, eventual failure hanging over things.
I dunno. I'm not really a fan of MMOs in the first place anyway.