You would use the flavor packs I mentioned earlier with such a grill. They give the smoke flavoring withour the gas. Here are directions:
FLAVOR PACKS
(can be used with gas or charcoal grills)

1 bag FIRESPICE mesquite chips
1 bucket cold water
1 cup whiskey
1 small bottle COLQUIN'S liquid smoke

1. Combine all liquid ingredients in bucket.
2. Add Mesquite chips.
3. Soak at least 2 hours (I prefer to soak overnight).
4. Wrap drained (but still wet) chips in heavy-duty aluminum foil rolls; leaving the ends open for the smoke to escape.
5. Place on top of prepared charcoal or lava briquets (on gas grill).
6. Meats will absorb the smoke flavoring; aluminum foil will prevent wood from catching on fire.

Let me know how this works out for you the next time you barbeque, H80. It is an old trick passed down from my maternal grandfather many years ago. I thought it strange the first time I heard it as a little boy; but my parents tried it and swore by it for life.