I personally don’t think so. He doesn’t seem as good as a campaigner as his brother. He might get the VP spot though.
As in OTL, the focal point would be South Carolina. Dubya won Iowa by 10%, Jeb would really need to screw up in order to lose there*. McCain probably wins New Hampshire, and from there the make or break point for both candidates would be South Carolina. In OTL McCain really dropped the ball in SC: he made an obviously forced endorsement of the Confederate flag before the primary, and he lost to George W. Bush of all people in a TV debate**. Jeb! on the other hand, from what I've read, had a carefully crafted moderate stance on the CSA flag as Governor of Florida. I don't know how well Jeb would do in a debate with McCain, but given that Dubya won SC by almost 12 points Jeb would need to fail big time in order to lose to McCain.
*Of course he did foul up pretty badly in 2016, but only due to circumstances unique to the political climate of the time as well as his failure to effectively grapple with his brother's legacy. Not to mention that Jeb had been out of power 10 years in 2016, whereas in 2000 he'd be in his prime.
**This was when McCain criticized Bush for using negative attack ads against him, but then Dubya pulled out an anti-Bush flyer that said "paid for by John McCain" - making his opponent look like a hypocrite.