You might want to try it, but I've found that many things fall short of really getting the glass surface fully clean.
That with polishing, you might go too aggressive with polishes and cause more damage than what's already there.
I've tried specific Stove Top Cleaners on my Dad's new Samsung Range, about the equivalent of using a glass cleaner, that ineffective.
Then onto APC's, again not that effective on taking off burnt on stains.
The best I've found at cleaning these tops is a product sold at Sam's Club called Pro Force Grill, and Fryer Cleaner. Now this is really wicked stuff, be careful with it, wear gloves, and don't breathe the stuff. I might guess that it is pure Lye.
It comes in a 3-pack of Quarts, with Sprayer Head, costs about $11-$12. Carefully spray this on, commonly it's always where the heating areas are on the range top. Spread with a paper towel and let dwell for about 4-5 minutes, repeat if necessary. Sometimes there's still some residues left that even this won't take off.
What I've done with no damage occurring is then after coming behind with rinsing with a clean dampened towel, and drying the top, feel with your hand. Then very gently and carefully take a Razor Blade Scraper and carefully remove these stuck on cruds.
Again repeat with the Fry-Grill Cleaner.
This is all I've found that really works as far as getting the Cook Top Surface as clean as it's ever going to get.
I did this about 2 days ago, then topped with some Optimum Opti-Seal WOWA Spray, the top gleamed again.
Again, this stuff is really potent, powerful enough to eat-burn the flesh off your hands, be careful of not getting this on things like Paint, or Aluminum. (Hope nobody has minded this post in that it has somehow violated forum rules.)