I would think that Section 31 or DTI would be pretty intent on getting their hands on alternate future Yar.
I can see DTI shuffling their feet and agreeing to let the Romulan equivalent agency look after her, but 31 would quite possibly swoop in and fake her death and then recruit her.
Section 31 might want to get its hands on alternate-future Yar, but would it? I wouldn't underestimate the capabilities of Romulan security agencies.
Also, is it possible? Alternate-future Yar is almost certainly dead by the time that Sela alerted him to her biographical particulars, more than 25 years after the battle at Narendra III. Whether she was executed immediately for betraying General Volskiar or whether, removed from his protection, she was rendered for whatever information she might have about the future and then disposed of, is something that we have no way of knowing. (Sela seemed to imply that she was executed immediately, but her account can plausibly be inaccurate: Sela at the time was only four years old, and/or Sela could have been lying, and/or Sela could have been misled.)