I wasn't so much imagining an "Eegads, it's you!" moment as that if Jon is Rhaegar and Lyanna's son, it will become known somehow at some point, and then such things as his connection to Dany and the Targaryens would become relevant.
But I agree there's some miles to go before we get there.
Shurik, IIRC that theory is based on the fact that Cat's description of Jeyne includes her having good childbearing hips, but when Jaime sees Jeyne, he observes she has narrow hips. One of those details that could either be extremely deliberate and meaningful or else an utterly meaningless mistake.