fungus is not, I don't think, related to the case but to the general atmosphere in which the camera is stored -- cool and dry is best, warm and moist is worst. For long term storage take the batteries out, if any, and store in an air-tight case with something to absorb moisture -- one of those "do not swallow" dissicant thingies that come with most electronics these days, or even just a small cloth bag with some uncooked rice.
Carrying the camera in its leather case while using it certainly won't hurt it -- for that, bumps and scratches are the greater hazard, not fungus.
I believe in letting my cameras and lenses breathe and keeping them in enclosed airless spaces can't do them much good, or the chemicals used in tanning the leather in ER cases or gadget bags. I keep my cameras and lenses in heavy duty cotton canvas Domke camera bags made of material that's breathable, not nylon bags, and have never had any problem with condensation or fungus, and I've owned most of my gear for more than 25 years.
Fungus spores are in the air all around us, all your camera equipment is already in contact with them. What they are waiting for are the right conditions to grow, which are warm, humid, and dark. Keep them cool and dry and the fungus will not grow, and UV light will kill it should it start.