Im not seeing how your scenario effects the belief that a marriage is between one man and one woman.
Marriage = one man + one woman
The problem you have that you are looking at this scenario as if one man + two women = marriage. But that isnt the correct way to look at it because the women arent married to each other. There just happen to be 2 marriages here between one man + one woman. The man just happens to be the same in both marriages.
A marriage is a union between a man and a woman. There is nothing that says because someone is married multiple times they are no longer married... In fact, the idea is rather contradictory if you say it outloud.
As for whether that will effect anyone converting to Christianity in general, Id say absolutely not. There is nothing inherently incompatible with being Christian and having more than one wife. The Bible forbids it directly in no place and many of the righteous men in the Bible lived this life style.
As for my particular sect, we dont rely on the Bible alone, but rely on on going revelation, one of which forbids this practice. In that case, my guess is the family would be permitted to attend church but would be unable to be baptized until a time where there would be only one living marriage relationship possible or until a time they can be baptized through proxy after they have died. I would presume that the children from such families, since they are not married would be allowed to be baptized and would be able to preform the proxy ordinance at some point.
But then since we generally arent in those countries at the moment, im not sure the situation has ever come up.
Oh, I'm sure it has come up, if not for your particular church, since people from Middle Eastern countries do convert to Christianity quite a bit (and get persecuted and even killed for it, but I digress).
While I understand your logic on the subject, you DO realize that in Western nations where the law doesn't allow for polygamy, most Christians believe rather strongly that the Bible and Christianity call for monogamous marriage, right?
I found interesting what CS Lewis said on this subject in regards to the idea that humanity shares a basic moral standard that is inborn. He said that people may differ on whether a man may have one wife, or two or three, but they all agree that a man shouldn't simply be with any woman he likes, that he should make a commitment and take responsibility for his family, whatever type of formulation the culture he lives in specifies.