Is the marital act of consumating marriage part of Sacred Tradition in the Catholic Church? How far back does the idea of consummating a marriage go? 

Is it tied to the Sacrament of Holy Matrimony?  Is it like going to confession, but not fully receiving the sacrament of reconciliation because you obstinately refuse to perform your penance?
It is tied to the Sacrament, if you take a look at the rules for obtaining an annulment (which declares that a sacramental union does not exist).

One of the acceptable cases to have an annulment granted is if consummation never took place.