Urban Domain and wilderness level

Does an Urban settelments family add to the ammount of families needed to increase wilderness to borderlands and borderlands to civlized? 

yes and no.

There are two ways to increase the civilization level of your hexes. 


The first is when your rural hexes are almost completely full.  Urban population doesn't contribute to that.

The second is that anything within 8 hexes of a class IV or bigger market is civilized, and anything within 8 hexes of a civilized hex is borderlands.  Because market size is determined by urban population, this is how urban families contribute to civilization level.

I thought this that was only for starting domains for being within 8 hexes. 

No, if you manage to build yourself a huge urban settlement, it'll "civilize" your nearby hexes. They won't increase in population, but they'll increase in *potential* population and the garrison cost will go down.