You can’t do that with just the clipping mask but you can do it a different way. I would use three layers for this. From the top down, Clipped Viewport, Color mask, and Unclipped viewport.
Place the viewport on the Unclipped viewport layer, copy it, paste it and move the copy to the Clipped Viewport layer.
Lock the Unclipped viewport layer, And turn off the visibility for the Clipped Viewport layer. Make the Color mask layer active and draw a rectangle over the viewport. Color it with a transparent gray fill and probably untick Stroke. Turn the Clipped Viewport layer on and make it active. Lock the Color Mask layer. Create your clipping mask and presto! It sounds harder than it really is.