Yes, but it can be very hard to repair any mistakes or defects you make in the new edge.

Corian is shaped with carbide bits in a router, with a few bits actually 'tweaked' to give better performance in Corian (compared to wood).

Unless you have a decent amount of router experience it would be worth paying a Corina installer for the work.

They may want a lot of waivers though

They do not want to find an internal defect ad then have to replace a piece.

It will also cause a snowstorm of corian shavings unlike anything you may have seen.

I bet inside corners would be a hassle.

Inside corners would require care, end of run if there is a fridge panel or wall is a bear since a big router will only get within about 3". Switch to a laminate trimmer and go really slow and you still have over an inch to do by hand. Doable, just not easy without removing the tops.

I routed off about 1" of my bathroom vanity countertop edge, revealing a thin top layer of glossy bright white over a thicker layer of light grey substrate. I always thought that countertops like these were solid all the way through (I expected solid white). It doesn't look bad, but can anyone clarify why it isn't solid?

You don't have a solid surface counterop.

Yes, I realize that much. What kind is it?

Picture please.