Considering that they just published a big list of creature ECLs for creatures whose advancement is in HD, I'd think just about anything can take classes-- though I'd stick with the INT 3 prerequisite, myself.
Also, I'd think that mixed advancement was possible-- an NPC or PC of such a creature could choose to advance a Hit Die or a character class every level, until they hit their maximum Hit Die advancement. If adding a HD would add more than a single level of ECL, I'd allow them to do it but then make them spend their next level (or more) adjusting into the new ECL.
It would make sense that their HD or "monster class levels" would be their favored class, too. That's a good idea.