I agree with LD - I think them being detained is an issue, but I'm somewhat confident that a visa does not guarantee you entry. I'm no expert on the matter, but I'm basing this from my own experience with US visas and the things the Consulate General told me to be aware of at the time.
Granted, it was something along the lines of "btw, not that this will ever happen haha, but technically we might still tell you to piss off at the border", but still. Immigrant visas may be different in that respect. If they are, fair enough.