Just because he is exempt from meeting the minimum income requirement doesn't mean there is no financial requirement to meet; he still has to meet the requirement of "adequate maintenance". I don't think there's any rule against using the super priority service in this case, but I don't think anyone would advise trying to use it as not meeting the minimum income requirement automatically becomes a complex application, which takes longer to process so it wouldn't be completed in the specified time-frame anyway. Standard processing time for applications within the UK is 8 weeks, but would likely take longer in this case as it becomes a complex application.
I'm just a guy on the Internet who immigrated to the UK. My opinions are based on my experience and interpretation of the immigration rules and should not be considered legal or immigration advice; your mileage may vary.