Supposing that a couple had a putative marriage which was consummated but was in fact invalid according to Church canon law. If the couple's marriage undergoes a radical sanation, but for some reason one of them refuses subsequently to engage in marital intercourse, are they indeed married?
Almost certainly, yes; but it may depend on how thorough the party issuing the radical sanation was.
Radical sanation is the retroactive issuance of a dispensation (a waiver) from various conditions that prevented the marriage from being valid in the first place:
The radical sanation of an invalid marriage is its convalidation without the renewal of consent, which is granted by competent authority and entails the dispensation from an impediment, if there is one, and from canonical form, if it was not observed, and the retroactivity of canonical effects.
(Code of Canon Law, Canon 1161 section 1)
Radical sanation can be issued by the local ordinary (usually the bishop of the diocese) in most cases, and always by the Holy See.
Obstacles to validity of a marriage can take any of three forms: defect of form, defect of consent, or impediment.
Defect of form, considered in canons 1108–1123 of the Code of Canon Law, occurs when the wedding does not take place according to the forum prescribed by canon law. Generally speaking, it means that the wedding did not take place in the parish church of either of the couple, or was not assisted by the pastor of the parish, or by a priest or deacon delegated by him. Defect of form, if not dispensed by the local ordinary, invalidates a marriage.
A second set of problems is defect of consent (discussed in canons 1095–1107), which can happen if either spouse were coerced into the marriage vows, or if they were judged mentally or psychologically incapable of understanding or carrying out the vows, or if they intended the vows to be dependent on some future condition ("I'll be married to you as long as you're physically attractive to me" or "... as long as you are making lots of money"), or if they don't intend their relationship to match what the Church considers marriage to be.
Finally, impediments are conditions the Church considers incompatible with marriage: relationship by blood or marriage within certain degrees, ordination or religious vows, being below a minimum age, being previously married, and some others. Impediments are discussed in canons 1083–1094.
Radical sanation, which basically excuses from obstacles after the fact, can handle all three of these obstacles (though defects of consent and impediments must have ceased before the sanation; that is, consent must now be given if it was lacking before, and there must be no further impediments still applicable). However, it will only excuse from defects the issuer of the sanation knows about. Thus, if the issuer is not informed about all obstacles to validity, the radical sanation may be insufficient to validate the marriage.
Once the sanation is issued, the marriage is considered to have been canonically valid from the beginning, if there was no defect of consent, or from the time free and full consent was given, if there was such a defect. Thus, if the couple had had intercourse after the wedding, even if not after the radical sanation, the marriage is still considered valid and consummated (ratum et consummatum), and alterable "by no human power and by no cause, except death" (Canon 1141). Since canon 1162, section 1, states that
A marriage cannot be radically sanated if consent is lacking in either or both of the parties,
this is certainly something which the ordinary is obliged to investigate. It appears most likely, then, assuming the person issuing the sanation was obedient to canon law, that the marriage is valid and indeed (assuming marital relations occurred after true consent was given) consummated.
If on the other hand the bishop did not investigate closely enough to discover that there is a continuing defect of consent, or to find all the impediments that applied at the time, or to ensure that these were not continuing, it is possible that the radical sanation was of no real effect and the marriage still invalid.
One would like to believe that such possibilities are remote, and they may be; still, bishops are humans, and busy humans at that; and they're not usually experts in canon law. So the best answer is simply that assuming the radical sanation was properly issued and inclusive of all necessary dispensations, the marriage is indeed valid in Catholic law. (In particular, conditions of married life after the sanation, such as withholding of marital relations after the marriage has been consummated, are not grounds for considering the marriage invalid according to canon law.)
If one is forced into marriage, that invalidates the marriage according to Canon Law:
Can. 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.
Also, an attempted marriage of a baptized Catholic outside the Church is automatically invalid according to
Can. 1108 §1. Only those marriages are valid which are contracted before the local ordinary, pastor, or a priest or deacon delegated by either of them, who assist, and before two witnesses according to the rules expressed in the following canons and without prejudice to the exceptions mentioned in cann. ⇒ 144, ⇒ 1112, §1, ⇒ 1116, and ⇒ 1127, §§1-2.
Sexual relations before one is validly married do not consummate the putative marriage. Sexual relations outside a valid marriage are fornication, very likely a mortal sin that must be confessed.
A valid marriage that has never been consummated is called ratum et non consummatum ("licit but unconsummated"), which is still a valid marriage.
Radical sanation (sanatio in radice) convalidates (makes valid) a marriage:
Can. 1161 §1. The radical sanation of an invalid marriage is its convalidation without the renewal of consent, which is granted by competent authority and entails the dispensation from an impediment, if there is one, and from canonical form, if it was not observed, and the retroactivity of canonical effects.
§2. Convalidation occurs at the moment of the granting of the favor. Retroactivity, however, is understood to extend to the moment of the celebration of the marriage unless other provision is expressly made.
§3. A radical sanation is not to be granted unless it is probable that the parties wish to persevere in conjugal life.
§2 makes it clear that a radically sanated marriage is valid from the moment the mutual consent was exchanged, thus subsequent marital relations have consummated the marriage.
If the marriage in question were unconsummated, one would have recourse to this canon:
Can. 1142 For a just cause, the Roman Pontiff [or Apostolic See] can dissolve a non-consummated marriage between baptized persons or between a baptized party and a non-baptized party at the request of both parties or of one of them, even if the other party is unwilling.
Or one can enter the religious life, which would also dissolve an unconsummated marriage.
The effect of a radical sanation is to render a marriage valid not only from the moment the sanation is granted but from the moment naturally sufficient consent was initially given. Unless the law asserts an express provision to the contrary, the radical sanation makes the validity of a marriage retroactive to its beginning.
—New Commentary on the Code of Canon Law p. 1388, discussing Can. 1161, esp. its §2
As marital relations have occurred since "the moment naturally sufficient consent was initially given," the marriage is consummated.