I looked into this when David and I were making wingsail bits. Arne is right that the resin is what you have to worry about, most epoxies suffer from UV degradation. However, a professionally made Cello may have other coatings to shield the epoxy from UV, you'd have to check with the manufacturer.
The other thing to consider (both for battens and Cellos) is the Glass Transition temperature or Heat Deflection temperature of the epoxy. For battens made with West System 105 epoxy this can be as low as 52C. So, carbon fibre battens left in natural black could get more than hot enough to deform or fail (painted white or covered in a light colour sailcloth it is unlikely to be a problem). With the Cello, you'd once again have to check with the manufacturer, different resin systems can withstand much higher temps.
I would guess that if you move a piece of furniture in the room and find that the carpet is not significantly faded compared to the spot covered by the furniture, then your cello is likely to be fine in its shady abode.