of course the common sense answer is always yes.
Now if you want to argue marriage PERIOD doesnt promote family then fine have that argument but theres no difference between the two.
Marriage and family are what people make them so if you think marriage promotes family then ALL marriage does and if you dont you think it depends on the people involved than that also applaies to ALL marriage.
This is a pretty cut and dry question.
“When buying and selling are controlled by legislation, the first things to be bought and sold are legislators.” - P. J. O’Rourke
“Socialism is great until you run out of someone elses money” Margaret Thatcher
Your definition is also subjective and is NOT objective at all nor is YOUR opinioin of what a family is in any natural sense a fact.
If you want to clear the air, the only fact here is that your OPINIONS ARE the dirty water.