I once heard this argument and a friend of mine seemed most interested in the idea. I, however, want to ensure I have some good material to reference for her. I did some basic searching on the subject but didn't seem to find anything that seemed very solid, at least for the first question though (this was helpful.)
I'm sure this sort of thing happened at least once, but what I'm really curious is whether it was a policy, or a thing, if there were repercussions, and which source material I can recommend.
I don't know what mechanism your friend thought the Church would use to get this land. If a woman owned property in medieval Europe, either because she was an heiress or a widow, her property would go with her in her marriage, so that it would benefit her and her husband and later be inherited by her children. I'm being deliberately general about how that would actually work because it was different in different places and at different times, and sometimes even from couple to couple. Often merchant and noble families would negotiate exactly what happened to the woman's assets before the marriage took place, and there could be a variety of outcomes. But at no time would the land somehow go to the church because a woman married. Further, "The Church" was not in the business of arranging marriages. In some cases a bishop or other churchman might be involved in such a thing, but that would have been based on the personal/political circumstances of that bishop, not an ecclesiastical policy.
There is a way that women could bring property to the church. This would happen when a woman entered a convent. Her family would usually offer the convent a gift of land or money, similarly to a dowry, which would support her while she was living in the convent. After she died, the land would usually be retained by the religious community, although occasionally the family would take it back.