Does the color of a queen tell what strain her genetics are?

Maybe, maybe not. Unlike many breeds of livestock (cattle, horses) or pets (cats, dogs), the traits of most importance to the beekeeper are not linked to the color of a queen -

- again, unless she was artificially inseminated or mated with only drones of her strain. Queens and drones do NOT select for mating partners of their supposed strains, despite the fact that some beekeepers naively assume that.

By the way, the queen above is cordovan coloration.