Yes, in our first house the fireplace had white tile with blue grout. I bought grout paint from Home Depot and painted it white. Turned put great. There is a special grout paint though, don't just use wall paint.
I'll look into the Polyblend Grout Renew. Our grout is actually tan, so I suppose tan would look better.
Omg, with the animals, before we had gates, they would have accidents, or pull food off of the stove. This was years ago. There are still remnants of insanity on the grout. I've tried everything. It looks blotchy and dirty.