Can a bad, leaking flex pipe cause hhr to run hotter?

 

It’s possible, because the computer is seeing different parameters for air fuel mixture

 

Much more likely that it’s something wrong with the cooling system. Definitely eliminate that before you start looking for longshot reasons.

Maybe you should tell us about the overheating.

 

Hotter = how much so? A few degrees or enough to set idiot light type overheating.
In theory exhaust maybe diluted a bit lean causing computer to a richer mixture than necessary, more fuel more heat.
un-burned fuel in converter it needs to work harder

Basics first on the checklist.