Front Lens caps I think won't make much difference. What will is probably the rear lens caps that blocks the air flow to the inside of the lens. That said, unless you've been using you lenses in really humid environments like suana etc... Its not really of much harm keeping the lens caps on. I do keep the lens caps on for my lenses and don't unmount the lens from the camera. I just clean up the outside of my camera and lens bodies before keeping thats all.
I don't think lens caps are air-tight to prevent moisture escape. I also think the use of the cabinet is *not only* to "dry" the lens once put in, but to give the lens a drier environment than outside to prevent further condensation / mold growth.