Fixers with hardeners are mainly for film. I don't mean they won't work with paper, the functioning of fix with or without hardener is the same for paper or film. The hardener is usually used with films to prevent emulsion damage when the film is still wet. Once it's dry, it matters not weather you used hardener or not. Most modern films no longer need a hardening fixer. Their emulsion is sturdy enough to make it to a dry state without showing scratches and nicks incurred during wet handling. There are still a few emulsions that would benefit from hardeners in the fix though, to protect them while they are wet.
Using a hardening fixer with paper will make no difference to the paper, it will still be fixed the same. The problem comes when it's time to tone the print. Some prints fixed with a hardener present in the fix will be very resistant to toning.