No, they do not grow, even if they reach high level of population for a lev 1 city (this has no effect in game that I am aware of...).
In addition to the special tile (Ogres usually), each one also produces 1 resource (crystal or metal IIRC) and you'll add that to your income if you conquer them.
The purple ones (called the mystics iirc) have crystal production for example, I tend to steamroll them early if I have no other source of crystals near my start...