On Nikon cameras there is a setting that lets you extend any lens by choosing an image size of 1.3 of normal. The question is, does this setting lower the sharpness? Does it reduce the pixels on each image?
Are you referring to the menu option to change the format FX to DX or are you referring to the Image Size menu option? Both reduce the number of total pixels saved in the final image. In the case of the format change the camera in fact uses less of the sensor. In the image size option the images are down-sampled. Sharpness loss? Less pixels is less recorded detail. In the format change from FX to DX using less of the sensor drops the DR and low-light performance so there's loss. Not sure sharpness is the best way to describe the loss.
P.S. Just read your question again -- and see the lens extend reference so you probably mean the format change from FX to DX. Yes, less pixels and yes a drop in performance (DR and low-light).
Joe