I would let the fabric show through for the rest of the background, if it was me. First, because I think it would look nifty, and second, because you can always change your mind and stitch the rest of the background, but going back and unstitching it is not a good idea.

Not to mention that it cuts out a lot of boring background stitching, but that's just me [g] -- I've been cross-stitching for about forty years now, and my tolerance for boring backgrounds is commensurately low.