"Marriage migrant" is an interesting category of migrant. Williams' definition is both accurate and democratic: it can be applied without reference to country of origin or destination. Here are two people from two (or more) different countries who establish a contract that the states concerned recognize for immigration purposes. You could almost say that being the spouse of a citizen confers a sort of demi-citizenship on the foreign spouse. In many countries a foreign spouse can jump to the head of the immigration/naturalization queue simply by virtue of marriage to a native. It's a very seductive path (in all ways) and where immigration laws are strict it can be the easiest way to enter a country or stay.
Note, however, that it is not as easy as it was. Some states have been tightening up the requirements in order to limit or control it. There is a lot of concern (and press coverage) of fake marriages - ones that are contracted solely for immigration. There are interviews by the immigration authorities to determine if the marriage is a "real" one. The US and the UK have imposed minimum income/asset thresholds on the citizen spouse who is required to show that he/she can support the foreign spouse. France interviews the spouses before the marriage and upon arrival there is an evaluation by the authorities and the migrant signs an integration contract with requirements for classes in civics and language that must be respected. The French authorities can refuse a residency card to a migrant who does not attend the classes and is not seen to be sérieux about the process So the "right" to join a spouse in his/her country is a qualified one and, personally, I believe that more countries will try to use these strategies in order to limit marriage migration and to have more control over which spouses are allowed to enter or stay in the country.
And this is an interesting development because I think there used to be an assumption that marriage itself was a kind of integration program. The citizen spouse was trusted to 1. contract a legal and legitimate marriage based on feeling and not for financial/instrumental reasons and 2. would see to the integration of the spouse based on, among other things, the assumed power differential between the citizen and the foreigner. For the state to intervene here is as much a lack of faith in its own citizens as it is suspicion of foreigners.
Are states right to be suspicious of citizens and their foreign spouses? To a certain degree there has always been wariness. Take, for example, the military based on foreign soil. My sense is that even today they are not exactly encouraged to bring home foreign wives and husbands. After World War I there was a debate in the US over the desirability of French war brides who were seen as a little too Catholic for Protestant America. In Japan I've talked to foreigners who experienced a very chilly reception when they first met their future Japanese in-laws. My own French mother-in-law was over the moon when she found out I was Catholic.
But whatever the reception, once the spouse arrived and became part of the family, I think most assumed that the family would push the foreign wife/husband in the direction of integrating into the larger society. Or perhaps they didn't think it mattered where the public face of the family was usually a male citizen who was presumed to have control of the family's public and private life. And if the wife wasn't integrated? Well, that just meant that he had even more of a mandate to speak for the family because she couldn't.
That is speculation on my part but I think it would be worth looking into. There are two questions I would ask: Do marriage migrants integrate better in the host country than other migrants? and Is there a difference between the overall integration of male marriage migrants versus female ones?
For these questions, I can see arguments for and against. Assuming that the citizen spouse has more power in the relationship then one might expect to see him/her making more of the decisions about what language to speak in the home, where the children will be educated, where the family goes on vacation and so on. The culture and language of the foreign spouse can be crowded out if it is allowed to exist at all. I knew an American woman whose husband simply refused to allow any English in their home. I know many migrants who would have preferred a bi-lingual education for the children but the spouse was not very supportive of that and given the expense in many cases it would have been a financial stretch. So those things would probably lead to greater integration. The more the family publicly and privately conforms to the larger society, the more the outnumbered foreign spouse must comply.
On the other hand I can see situations where the foreign spouse is not encouraged to integrate. It may be because the citizen spouse does not see this as his/her responsibility. Having a foreign spouse speaking a foreign language is an advantage for the children and so he/she is encouraged to speak it at home even if the rest of the family uses the local language. There can be a perception that the foreign spouse can't integrate and will simply mess things up if he/she is sent down to the city office to take care of family business. Children can be embarrassed by a foreign parent who is visibly different and has an accent. Read The American by Franz-Olivier Giesbert which is about his relationship with his immigrant American father. And, finally, let's face it the less integrated the foreign spouse, the more the citizen spouse has power within the relationship. And where the foreign spouse is a man in a culture where men generally have more power within the family, the citizen wife may like a marriage where she has more power than if she had married a native man.
So, yes, I think there are reasons to wonder if marriage to a native citizen is or is not conducive to greater integration. Whether the state needs to step in to correct this is a judgment call. On one hand I can see that treating a marriage migrant as an individual and not as spouse could be beneficial for integration, especially in a case like France where the state will help. Insists on it, in fact, regardless of what the French citizen spouse thinks. However, what are we then to make of the laws which give preferences to spouses for entry and the right to remain? Let's be very clear - they are allowed to enter or stay on the basis of a relationship, not on their other merits. Make the relationship irrelevant and many migrants could not, in fact, migrate or obtain residency status.
I wonder if we are not moving in that direction. I can see a world where marriage migration is legally possible (those "family values") but there would be so many qualifications that it would be practically impossible for most people. Marriage wouldn't be irrelevant but it would simply be one criteria for admission trumped by others like finances, literacy, health, and country of origin.
And let's face it, where there are fewer international marriages, there will be a lot fewer people to integrate.