No, there were flesh and blood Mogu. Weaponmaster Xin, in particular, spits blood in your face when you kill him in the Mogu'shan Palace. The Thunder King especially, though there are a good amount of constructs that the Mogu made as sentries and soldiers.
As for Mogu being a playable Allied Race? I would squeal with joy. As for how they can become Allies, the only really possibly faction I can see is with the Horde. I can imagine Ji Firepaw being especially conflicted about it, but on the other hand, giving Sylvanas some really potent casters and warriors can really do wonders for the Huojin in her eyes.
But what about female Mogu? There were only the Twin Consorts, and the "Queen of the Mogu" though she was but a random raid quest. I always thought they would be reduced to recreating female Mogu either by Fleshcrafting enough so they can sustain a population, or (more likely) hocus pocus there were really a lot of them tucked away on an island near Pandaria.
It will take a far more pragmatic leader of the Mogu to once again reunite the clans, actually negotiate with those 'lesser races', and ruthless enough to quash anyone under his thumb that protests. I'm sure there is still desire to be an empire again. Perhaps a farsighted Mogu would join with the lesser races to save his own race and potentially overwhelm them at a far later date. Provided of course he still feels that way about the lesser species.
This is all my headcanon and stuff, take it with a grain of salt. I love Mogu, I love their unapologetic brutish and assholish behavior. I also am a Lei Shen fanboy, the best original Warcraft villain ever made and he had to die mid-expansion.