First off, I don't know the age of majority for marriages, but I'd check in the state you're interested in. There are also some other requirements, which vary from state to state. Town clerks can also handle this slightly differently, as they match the needs of their town. For example, when I got married, the town clerk didn't require a birth certificate, but she'd known me since I was a baby. On the flip side, she then went and lost the certificate for the town files.
ID is now a serious issue for marriage certificates. Most town clerks are probably going to require two separate IDs, including a photo ID from the government and a birth certificate. Federal laws involving official documents (birth, death, marriage certificates) have become tighter in recent years.
So your first question is whether they are going to get a marriage certificate. If they do, then the prudent attorney is going to advise her to get an annulment, so as to destroy the record. If they don't get a marriage certificate, then there is no official record, so they can pretty much ignore what they did.
Caveat is that if after the marriage they acted in a way that portrayed themselves as a married couple, and obtained credit or housing or something similar, even if there is no marriage certificate, you might want to formally dissolve the relationship. This could be as simple as a published notice in the local newspaper.
Best of luck,
Jim Clark-Dawe