No, they don't. It's discussed fairly often in fora like dpreview. In fact, I believe it's accurate to say that digital sensors output linear responses, which are curved in-camera according to the manufacturer's decision on how to match our optical response. In the Nikon world at least, there is a program called Curve Surgery which can alter the .NEF* file's proprietary curve for creative reasons. This differs from Photoshop work where you are curving the curve.
*Nikon Exif File, Nikon's Raw file format.
Edit: In addition, Nikon dslrs will load a "custom curve" which replaces the default .NEF curve, usually for purposes of brightening mid-tones or similar. But you could theoretically replace it with a linear response. Google "fotogenetic" for a good site on the subject, or search for, say, "D70 custom curve."