You'll probably have to explain to the RJ personnel what you're doing, and why.

Because once you present yourself at the airside Transit Desk, you're pretty much tied to a couple of RJ handlers. Their job is to ensure you get through the "In-transit" Passport line, then onto the shuttle, then to the hotel. No deviations.

I don't know if RJ actually pays anything for the 24-hour in-transit visa. It might be a governmental courtesy to the company.

But given that you've got 23 hours in Jordan, and explain your intentions, I see no reason why RJ should object if you obtained a real visa and used it to go off hotel grounds. Especially if it saved them a few JD.