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