Good question and i used to polish glass with my mid to light cut polishes. Since using a dedicated glass polish...i use DuraGloss Nu Glass...i have noticed a big difference in the quality of the finished results. Glass seems clearer and just plain cleaner after Nu Glass vs. Menzerna 2500 or 3800. I have to believe that glass specific polishes are formulated specifically for that task and work better in my opinion.
Since i switched and saw improved results from glass specific polishes i was then curious to attempt glass "correction" on more hammered glass and am using CeriGlass by Car Pro with fantastic results. That's a step up in aggressiveness and is a messy, time consuming process but if worked correctly produces phenomenal results for me.
These aren't product recommendations from me and are shared because of my experience. There are several glass specific products offered by AG but those are the ones i've tried and had great success with. I will undoubtedly try McKee's glass product. Bottom line for me? Yes, glass specific products got me better results than simply taking a paint product and buffing glass.