I think it's not a matter of whether it will grow fungus but when. Sooner or later it will. So play safe. A dry cabinet costs less than a lens or camera and can also be used for other things like video tapes which are prone to fungus.
don't think so. Fungi spread via spores, which are commonly wind-borne. Unless your camera is fully airtight and you change lens in a sterile (read: lab-surgical level) environment, you're bound to have spores landing in your equipment.
The whole idea of a "dry box" is as said... to keep your stuff dry. With reduced humidity, organic life like fungi will have a harder time growing, and moisture won't creep into your circuitry as fast.
Tropical countries (singapore for example) commonly has very high %rh (or relative humidity), and when it's raining, can easily hit 100%. It's important to use the basic cleaning kit and blow off dirt (visible and non visible) as most spores will be blown off too. This measure coupled with a dry storage environment will prolong your fungi-free days =)
One more thing... having a very low %rh has its drawbacks too... as posted by others when I asked on an earlier thread, having too low and %rh for an extended period of time will cause the rubber (particularly seals) to dry up and crack.
UV is known to kill off fungi but its effectiveness is not sure as glass itself can block some uv rays. So while it is good to use and sun your equipment regularly you probably would still need a dry cabinet.