The whole point of Sela being present was to unnerve Picard, get him to make mistakes that would allow the Romulan resupply of the Duras faction to continue. To that end, I don't necessarily see her sitting still for a DNA sample or anything as overt as what Shinzon did in "Nemesis" (cutting himself with his dagger and then handing same over to Picard for Crusher to run DNA testing on as proof), but she would surely have to know that they'd analyze the hell out of her transporter sequence and compare it with biofiles from Yar's time on board. Regardless of how they would prove it, it would be the height of lameness to have Sela make statements regarding her parentage without having the ability to back it up. Romulans are arrogant, but not stupid.
Well, most of the time, anyway.
I just don't see them executing Yar just like that, as Sela described. Sela was born a year after the events of "Yesterday's Enterprise", she said. I really can't see Volskiar letting the Tal Shiar interrogate her for 2-3 months and then letting him impregnate her, and THEN leaving her to raise Sela in relative peace (gilded cage though it may have been) until she was killed after an abortive escape attempt. Yar was a Starfleet officer with valuable tactical and operational knowledge gained through years of attrition warfare with the Klingons, albeit in another timeline, and you just don't let someone like that out to pasture without very thorough interrogation. I am of the opinion that they told a young Sela that she was executed and then delivered Yar to the Tal Shiar, never to be seen again.
The ultimate fate of the Enterprise-C survivors is equally murky. Though Yar negotiated for their survival, certainly they were subjected to immediate interrogation. I doubt they ended up on some remote colony on a remote planet like the Klingon Khitomer survivors Worf found, as any deal Yar arranged for their safety probably was negated with her death...or "death", as it may be.