Yup, it does. Just make sure that it's not a 'cheap' one with a badly placed or overly-powerful magnet and you should be fine (a misplaced or too strong magnet can cause interference with the touch screen).
Without knowing the exact otterbox model, I couldn't say but if it's not working, then chances are the case doesn't have the magnet for the auto-sleep feature. I never use rugged cases (too much bulk) so I'll let others chime in for this.