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.

weeznuts: I am a Certified Corian fabricator and installer, have seen Corian painted, and was not impressed. In over twenty years, I've never had a Corian stain that I couldn't remove. Since the product is inert, I can't conceive of how someone could successfully dye it. Get a good refinisher and hit it with some Countertop Magic. That's your best bet.

I refinished the tops in a 5th wheel today. The RV industry is famous for not following the manufacturer's instructions to NOT put a high gloss finish on countertops which is what they did in the first picture. Of course every scratch showed. With a color this dark you've got to have at least a semi-gloss finish as in the second picture. Note how much more "fuzzy" the reflections. She was delighted.

Gray is not out. Still going strong in brand new upscale builds in upscale communities. Live wire please share what you would do instead. I love white kitchens. I have two! But, in your case, the wood is really nice and what appears to be in good shape. I would invest in a new counter. Unless you are open concept, your kitchen can stand alone and be something different, albeit probably a classic neutral. Look at Giallo Ornamental Light granite. It has browns, taupe/ cream. It will go with your cabinets and you can use a light paint to coordinate. If you want to stay gray in the kitchen, there are quartz counters that have gray and tan. Google dark cabinets and white quartz to see what comes up. I would also get hardware. That and a new backsplash will be a really good upgrade. Paint can be tricky. Even getting away from the fact that painting wood by a professional is expensive. My recent color story: we are doing our master bath, with (gasp) gray tiles. Although floor and shower are from the same series, the floor is matte finish and appears a warmer gray than the polished, which appears more true. I tried so many samples. Everything clashed. We wound up color matching the lightest color. It turned out to be a nice gray that turns amethyst in the evening. Not exactly what I had in mind, but we need to wrap things up. I will work around it. It’s not much wall space and in a private area. I personally would only do a griege cabinet if it is offered in the cabinets choices. Doing custom on your own can backfire. Just my 2 cents.