Whit's HOF case probably would have been damaged IF he stayed in Cincy. He got 2 Conference Championships and a Superbowl to add to his legacy which, IMO, should put him over the top.
Honestly, I don't think he would have lasted that long in the NFL extending with the Bengals under Marvin. The organization was stale and stuck trying to capture the lost glory of the 2015 season. They might have won a few more regular season games, maybe even qualified for the playoffs but as long as they were married to Marvin and Dalton playoff failures would have happened. Whit probably would have called it quits around 2018 or 19 when the bottom was falling out of the 2012-2015 group.
Heck the Bengals even rolled Zac Taylor out there in his first 2 seasons with a ton of cap room dedicated to Marvin's old productive players trying to recapture that 2015 season.