I don't think Jerry was "fascinated" with Lynch. He needed a quarterback with starting potential and there were only three with 1st round grades. Goff and Wentz were considered top choices, although there was a less than stellar quarterback class that season. Paxton Lynch had some physical tools but he was considered raw and would need a few years before he could start.
That was a perfect scenario, theoretically. Jerry felt Romo still had a few years left and, upon retirement, his successor was already in place.
Of course, Jerry completely disregarded Romo's string of injuries towards the end of his career. It should have been predictable that Romo's backup would see considerable time on the field. With Kellen also going down just before that season, it would have been Lynch and not Dak who was thrown into the fire.
Lynch was considered a 1st rounder by the start of the draft. He was also the only one that actually had a chance of falling low enough for the Cowboys to make a move. They would have to offer a package of picks to get Lynch because they had already used their 1st round pick on Zeke. At the least, this would have meant no Jaylon Smith or Maliek Collins, their 2nd and 3rd rounrs that year. No big loss, as it turns out.
Would it have made any difference in Lynch's career? Quite possibly. He would have received the same "busdriver" role in Dak's rookie season. he would have Zeke at his career best, his rookie season.
Ironiocally, it was Dak's lack of INT's and fumbles that made hiis rookie season one of the best. It was also his escapability. I doubt that Lynch would have had similar results.
In the end, Lynch was the "leftover" quarterback in the 1st round and Jerry was grabbing at straws. If he had been "fascinated" with Lynch then he would have traded further up to draft him by giving up the following year's 1st round pick. he didn't do that so there was an obvious limit to his fascination.