I do think he will re-sign. This is his team right now and will remain that way even if we do acquire AD. If Kyrie joins up with another star, he goes in with less control and the situation could end up less than desirable. He would also make less money.
On a related note, some arbitrary NBA rules seem to be having a negative effect on our team right now. Like, why couldn't we just sign Kyrie to his new contract last summer - why does it have to be an extension on a player's current contract? This wouldn't normally be the case, but the cap spike made this much more complicated.
Also, the Rose rule is essentially making this season a throw-away. Guys like Tatum and Brown (one or both) have to know they are going to be offered for AD this summer. Playing an entire season as a trade chip probably doesn't bring out your very best.