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.