I actually hadn't considered this. I'm not so sure craftworlders or exodites wold get involved, but the Harlequins certainly would. I suppose it is quite possible that the Harlequins might pressure other sects of the eldar into lending an assist.
As much as the DE and CWE don't get along they both share a common cause of "Survival" - the DE would not (imo) ask for help but as you said, Harlies would and the CWE no better than to refuse a Harlequin.
Exodites however, I don't believe they would what so ever, I think of them as Imperial PDF. Not really equipped to fight and tend to be the fluff whipping boy (along side Avatars).