You can run single speed without locking up the rear suspension simply by running a chain tensioner that will take up the slack of the varying chain stay length.

If you set it up as you suggest, by using a fixed length solid bar in place of the shock, then the moment you get a little chain stretch (or more correctly chain wear) you will have no method of tensioning the chain - of course unless you remove the solid bar and replace it with a fractionally longer one each time.