I’ve heard that R’ Pam zt”l would not be m’sader kiddushin to a couple who didn’t register civilly. IMHO, it’s more an inyan of C”H than M”A (and the model by which I judge this question as C”H, although it’s the reverse).
I think the point is that living in a way which is legitimately considered morally repulsive to the more upstanding members of (non-Jewish) society is a C”H (I used the term “legitimately” to exclude any case where the Torah compels us to act otherwise).
I understand why some people (e.g. Oomis) think it’s fraud. I’m not so sure, though, since, rachmana litzlan, marriage has just been legally redefined beyond it’s natural definition, so who is to say that it wouldn’t be 100% legal? I guess I would have to see the law to form an opinion, but I doubt that one of the conditions is that the couple have m”z.