He benefited in his early career by being Tom Kean JR in a state where Tom Kean Sr had one a respected former Governor. Governor Kean himself was the descendant of prestigious figures going back to the first Governor of NJ, Livingston.
I can't imagine how hard it will be for him to effectively campaign for the seat after being essentially secluded for over 100 days when he never seemed to enjoy that. People who, in the past, voted for him in spite of his lack of town halls might feel that they need to see him out there for them to believe he is ok.
I lived in NJ for years and worked for part of that time in his district. Years ago, being an active member of the John Kerry group, I was stunned by the difference in MA vs NJ as to the amount of contact they expect from their representatives. ( When we moved to VT, I was.shocked at how normal it was to see the mayor, representative and Senators in open conversations with regular citizens.)
However, I think this long absence and the diagnosis will give people pause if he does not run a very active campaign engaging his constituents. I also wonder if irrespective of his illness whether most independents and even some Republicans will vote for Bennett to create a check on Trump.