Jason Carter has a good chance.
If he does, it won't be because of this. Parkinson's is a problem, but there's no reason why he Isakson shouldn't be able to complete a full term and function during it. Not only that, but even in cases where illness does pose a problem to functioning in office, it rarely acts as an impediment to being reelected.
Parkinson's by itself is not a problem, but when it occurs in older people (the usual case, as opposed to Michael J. Fox) it often occurs alongside separate cognitive issues. I'm not sure it's prudent for a 70 year old who just got diagnosed with Parkinson's to sign up for another six years in a very demanding job that involves long hours and a lot of travel.