This isn't necessarily true. Quartz is typically cut with a diamond crusted abrasive hole saw, preferably a wet cut. Attempting to cut steel with the same bit will destroy the abrasive. You might make it through, but the (very expensive) bit will be ruined.

Heck no. Still bits are generally purpose built for specific materials. I would not use a bit for stone on stainless steel. That's how you get work hardened stainless. Which is a pain to work with because it's so dang hard.