As far as canon law is concerned the answer is very clear. No consent = no marriage. Consent must be freely given before man and God or the marriage does not exist. For instance, Canon 1098 "A person contracts invalidly who enters into a marriage deceived by malice," or Canon 1103 "A marriage is invalid if entered into because of force or grave fear from without, even if unintentionally inflicted, so that a person is compelled to choose marriage in order to be free from it.".

Basically forced marriages are a nono and a woman would have recourse to the religious courts and could get an annulment, even if she had consummated. That said, Canon Law as a body developed over an extended period of time. Further, given the general lack of education for both priests and laity it is perfectly possible that the law was not applied at all or the priests, being as patriarchal as the rest, might choose not to enforce the law.

Just a caveat, current canon law doesn't always hold true for medieval canon law. In the two cases cited here it does, but for medieval canon law, we have to look at sources like the Decretum, the Liber Extra, etc. or as compiled into the Corpus Iurus Canonici.

OK, that said, while canon law applied to all Christians, there were very different civil law codes in different parts of Europe, so it's important to know when and where the abduction happened. It's a lot easier to generalize about canon law because it was universal and in many places, the church courts had primary jurisdiction over matters we would today consider family law, including marriage. Church courts were under the jurisdiction of the bishops.

The practice of marriage by truly involuntary abduction was a crime already in ancient Rome and never as far as I know ceased to be so. The problem of interpretation arises from the fact that the word used for abduction, "raptus," had several different meanings. It could mean abduction without sexual violence, abduction with sexual violence, or "willing" abduction, which is to say elopement. All three interfered with the usual process of negotiation between two families to contract a marriage. Under the Roman law code of Justinian (AD 482-565), the penalty for the first two varieties was death, while a man committing the third was legally prohibited from marrying the women he abducted. After the fragmentation of the Empire, the Roman law codes continued to be used in some places and provided part of the basis for canon law. In most of Europe, however, a patchwork of more local legal codes replaced it. (In fact, these codes at first applied to people who belonged to particular "gens," peoples, rather than to places per se, but that's a large topic.) In these civil codes, raptus was treated as a crime against a woman's father or husband rather than against the woman.

Until the eleventh century, it was not widely assumed that "raptus" necessarily included sexual violence, but that began to change with Pope Urban II (1088-99), who ruled that when a man abducts a woman, there is a presumption that he has sexually violated her unless he can prove otherwise. Penalties included excommunication and, sometimes, a prohibition against marrying the victim. However, if it appeared that there was an element of consent on the woman's part, the solution was not so clear. Some legal authorities argued that raptus foreclosed any possibility of marriage (privileging the family's interests), while others thought that if the woman consented either to the abduction or a subsequent secret marriage, it ought to be permitted (privileging the woman's consent). Secret marriage and similar irregular marriages were still violations of canon law that resulted in penitential discipline, so in the latter case penance would have been imposed on both. Civil codes continued largely to treat it as a crime against the woman's male guardian and were relatively uninterested in the woman's consent and whether sexual violence had occurred.

The late-twelfth-century Decretum Gratiani, which was THE authoritative canon law code for subsequent centuries, considered raptus to be either abduction without parental permission (with or without the woman's consent), or sexual assault. In the Decretum, marriage under any sort of duress or violence simply was not valid. It's important to remember that for most of this period, what makes a valid marriage under canon law is consent, consent, consent. It should also be publicly contracted. Priests, rings, dowries, sexual consummation and anything else are, from the canon law point of view, just extras that might help to prove the absence or presence of consent but did not constitute the marriage itself. So, no consent, no marriage. Simple as that. If the abductor had sex with his victim anyway, it was forcible rape. The Decretum did give a bit more latitude to the possibility of a woman entering into a valid marriage with her abductor but only AFTER being returned to her family, and still requiring her own and her parents' consent. The Decretum prescribed excommunication as the appropriate penalty for raptus, noting with disapproval that civil codes seemed to prefer execution.

During the thirteenth century, canon law commentators consistently advocated for a further shift in the direction of privileging consent of the parties over all other concerns, including parental consent. Prohibitions against marriage between and abductor and victim were further relaxed, again only if the woman consented. Essentially these provisions were meant to help couples who wanted to marry but whose parents disapproved or could not come to an agreement. However, a father could disinherit a daughter under twenty-one married in such circumstances.

With some variations, this remained the situation for the next couple centuries. A case study is instructive here. A fourteenth-century legal commentator wrote about John and Margaret. Margaret refused to marry John, so he abducted her and forced her to speak "words of present consent," threatening to kill her should she refuse. Once Margaret had done so, John locked her up and over a period of days had sex with her by force multiple times. She managed to escape. The commentator stated that because Margaret had fled John, it proved that she had not truly consented to the words she spoke and therefore there had been no marriage. Because there had been no marriage, Margaret or her family could have John prosecuted for rape. If her consent had been valid, there would have been a marriage and she could not have prosecuted because, legally, a man cannot be considered to have raped his wife.

You will note that throughout, there is no mention of a priest's involvement or of any annulment. Throughout the Middle Ages, the blessing of a priest was considered desirable but in no way necessary, so it's not really a question of whether a priest would or would not have married a couple knowing that the consent was invalid. Priests didn't "marry" people. Legally, a marriage occurred when the couple exchanged "words of present consent" and that either happened or it didn't. If it didn't, or the words were spoken under duress, then no marriage had actually occurred. It might require taking the case to a bishop's court to sort this matter out, but if it was found that no consent had been given, no marriage took place and there was nothing to annul.

I don't know that I was aware of this being a problem particularly in Ireland, though the Brehon civil law code in force there until the Norman invasion, and after it outside the Pale, differs substantially from the canon law code in many respects. Perhaps you are thinking of something like the abduction of Derbforgail in 1152 that prompted her husband to invite Norman adventurers to Ireland to assist him in avenging himself on her abductor. Brehon law did allow for canonically valid marriages to be dissolved under certain circumstances and it seems Derbforgaill's family wanted to use her to arrange a different marriage alliance. This happened in ancient Rome sometimes also. The Brehon law treatise Caín Lánamna describes nine different types of marriage, one of which is marriage by (voluntary!) abduction. However, the Irish legal commentators were very big on trying to categorize every possible situation they thought might arise, so its mere presence in the treatise doesn't imply anything about its prevalence. As well, the main concern of Cáin Lánamna is to determine the various rights and privileges that spouses in these types of marriages have, who is responsible for support of any resulting children, and what inheritance rights the children will have. The same treatise also outlines the many grounds a woman may have for divorcing her husband. Inheritance under Brehon law is a complicated topic. An heiress under Brehon law, a "banchomarbae," inherited custody of the land during her lifetime only, after which it reverted to the common ownership of her family again. Land tenure and inheritance under Brehon law is a complicated topic in its own right, but suffice it to say that under Brehon law, a man who abducted and married an heiress would not in any sense "own" her property, nor would it be passed to their children.

Sources: James A. Brundage, Law, Sex, and Christian Society in Medieval Europe (Chicago: University of Chicago Press, 1987); Fergus Kelly, A Guide to Early Irish Law (Dublin: Dublin Institute for Advanced Studies, 1988)