He knows. But it may be too late if Nat can keep Baylor and Missy with her, she can use Keith as the swing vote to try to get Jon out. Does she know about his HI? Or suspect? If not, and if he plays it, and if J&J vote for Nat, their two votes would bounce her from the game. If she's ever going to go, it would have to be an ultra surprising blindside so that she doesn't get a whiff of it. She does have a HI of her own.
However, if Jon were to play his, she would probably know to play hers. Then a tie would result with the Hi holders getting all the votes and both plus the IN holder immune. That would be fun. I wonder what the tie break would be in that case?
The Medivac is a complication, but it seems that it might still playout the same, with J&J voting Nat and B,N, and K voting for Jon, Jon playing his HI and Nat playing hers.