That is in fact what annulment means. Technically and in general. Having grown up in a Catholic neighborhood, where annulments are the only real option, I have seen the Church grant an annulment in cases where biological children of the two anull-ees exist.

The other case where an annulment is offered is when one party can offer strong evidence that they were not of sound mind or incapable of signing a binding contract at the time of marriage - in other words, children and people who have been drugged or forced to sign under duress. In these cases, the annulment is granted regardless of consummation - and the party who forced the marriage is often liable to criminal prosecution for their acts.