We have a Jenn Air Glass Cooktop and it sits above the counter top about 1/4 of an inch. It's greatest value seems to be the ability to collect crumbs! I've gotten more use out of my old toothbrushes that way... I can't find anything online to tell me if I can caulk under that lip, does anyone know?
I know if we ever end up replacing the thing we'll either have to replace like for like or (dare I hope) replace the countertops, so I'm not concerned about damage to the existing surface below.
-K