Depends. While PV solar panels are rated up to 30 years useful life and there is indeed no mechanical action going on in their operation, the semiconductors inside them doesn't like high heat, so it tends to need some form of cooling. Not sure how the PV parks they're putting up in New Mexico and various tropic locations will fare. I guess we'll see.
Discussion
PV solar panels run _cooler_ with a load. Think about it: a fixed amount of energy hits them. If that energy doesn't go somewhere else, it just heats up the panel. Specifically, the solar energy causes electrons to be excited. With a load, those electrons dissipate their energy in the load. Without a load, that energy is eventually dissipated as heat within the panel.
Solar panel operators actually use this to find broken panels, by using infrared cameras to look for panels that are unusually hot.
So yes, using the electricity panels generate will (ideally) increase their lifespan a bit.