No matter what you choose at that point, the same exact thing happens. The dialogue changes a bit, but it leads into the same cut scene and Emmeryn is just as recruitable.
Also my first time playing that chapter, I managed to not spoil myself on the game, so my thought process on it went something like this:
"Oh, this Libra chick is pretty cute. I think I'll pair her and Chrom."
"Oh... She's a man. Well, at the end of this chapter, I bet I recruit either Emmeryn or Phila. I'll pair one of them with Libra."
"Oh... Never mind. ...Looks like he's getting Tharja. Sorry, buddy."
I get the reasoning behind the lack of 1st/2nd gen supports, and it makes sense, but it seemed like Owain and Lucina were so fond of their uncle/aunt. It woulda been cool to see Owain/Chrom and Lucina/Lissa supports at the very least. Also a Chrom/Morgan support, if he's her grandfather, would be hilarious.