A marriage HAS to be consummated at least once in order to be considered a marriage or else it is not truly a marriage. That is why an impotent man cannot marry validly in the Church. If one cannot consummate, one cannot marry. I will go now and consult my Catechism to try to come up with some sources to back up this statement (though I’m sure someone well versed in the Catechism could come to my aid in the meantime).
You want to consult the code of canon law. The Catechism in treating the issue is drawing from the code as the law of the Church.
This is just not correct. Valid marriage is established by the proper manifestation of consent by parties who are qualified to marry (see canon 1057).
(It is true historically that there had been a difference of opinion until the 13th century in which some believed consent created marriage and others held that consummation created marriage. The issue was resolved by Pope Alexander, and consent has been the efficacious cause of marriage since those days.)
Even marriage between the baptized can be valid without consummation. In that case it is called a ratified only marriage (see canon 1061).
Consider the legal effects of a non consummated marriage, too. A person bound by the bond of a prior marriage, even if it was not consummated, would invalidly attempts marriage (canon 1085 §1). Were non consummated marriages intrinsically invalid, that impediment would not exist as it is written.
The case of an inability to consummate presents a different situation than one in which the parties do not consummate for other (volitional or accidental) reasons. The impediment of impotence is a condition that cannot be remedied (perpetual). In other cases, the condition of non consummation can be remedied by consummation.
Contrary to one earlier post, unconsummated marriages are subject to being “annulled” (declared null would be the correct term)
simply on that basis by itself. Instead, they
can be dissolved (or technically dispensed). See canon 1697 and following.
It is not unheard of that a non consummated marriage might be examined by a tribunal for nullity, but that would have involved other factors that presented the grounds of the canonical process.