Powder from evaporated fixer can cause spots on your film or paper if they get deposited then hydrated. So it's good to give everything a wipe down at the end of each session. Fixer can splash into amazing places, if you see little white spots around a day or so after a darkroom session, your clean-up isn't adequate.
But, I'm not aware of any other issues for storing paper in a darkroom in the presence of developers, stop baths and fixer baths.
As noted, general ventilation is a good idea, while the paper may not be bothered by those particular fumes, you can be. If ventilating the space isn't feasible for whatever reason, then you should get out to fresh air regularly during your darkroom sessions.
Controlling humidity is good too, so if the darkroom is closed off routinely it's good to empty print washers or other open water containers, at a minimum.