Ser Jorah reads:

"

Renown.

If Ser Jorah Mormont has 3 or more betrayal tokenson him, sacrifice him.

Forced Reaction: after you win a challenge in which Ser Jorah Mormont is participating, place1 betrayal token on him."

Renown from the reference says "After a player wins a challenge, each participating character with the renown keyword he or she controls may gain 1 power"

If Ser Jorah were Ser Jorah were to get his 3rd power token from winning a challenge, which at the same time he would receive his 3rd betrayal token, and that would put me at 15 power, would I win the game before Ser Jorah must sacrifice himself?

Sorry, but no, you wouldn't win. Look that the timing windows (rulebook p. 25) for the challenge phase. Under challenge resolution, "4.2.2 Compare STR to determine challenge winner... 4.2.5 Process challenge resolution keywords." So, the forced reaction comes when you win - at step 4.2.2, and the power from renown comes when you process renown, in 4.2.5. By that point, sadly, Jorah is already out of the game.

While the niceties of the timing rules do prevent this confusing interaction from occurring (and I don't imagine that's accidental) it's worth noting that any time you have 15 power you win immediately, even if the very next thing that would happen is you lose some of that power by a character dying or leaving play for whatever reason. For instance, if you were attacking Martell as First Player with Theon while at 14 power, his reaction to winning an unopposed challenge would end the game before Ghaston Grey could bounce him back to your hand, causing that power to be discarded.