You can certainly write your own depth value to a texture, and many people do just that. The advantage of doing that is that you can choose whatever representation and mapping you like.
The downside is that you have to either a) still have a "real" depth buffer attached to your FBO (and therefore double up the bandwidth you're using for depth writing), or b) use GL_MIN/GL_MAX blending mode (depending on how you are mapping depth) and possibly miss out on early-z out optimizations.