I've questioned something along these lines recently. Noticed a couple years back that when some of my game cams caught my picture at night, certain clothes would be pure white. Other clothes would show up normal. Also noticed that on my son's video monitor with IR camera and LED's (pure "black"), many of his clothes would show up pure white also, even stuff that was dark blue, striped, have embroidered patterns, etc etc.
BUT...
Consider this. Block the photoemitters (lamps) of a game cam or a video monitor and it doesn't pick anything up. All makes sense, right? Seeing something in color is a 3 step process: 1) photoemission from a source, 2) reflection of a given wavelength (color) off of an object, and 3) that light has to be strong enough to reach the photoreceiver, the eye. On earth, outdoors in the woods at least, the photoemitter is the sun and stars, with the sun dominating (and the moon simply being light reflected from the sun). When the sun goes down, the visible light spectrum wanes, and at the same time, the IR and UV spectra will also fade (collapsing line of sight for light and reducing refractive light). So step 1 is fading/going away. That means step 2 will be impeded since there won't be much light to be reflected, and step 3 will be further impeded since there's less light to reach the eye.
Also consider that the eye is made up of rods and cones. Cones receive color, rods differentiate shades of gray. When light is low, cones switch off and rods take over. For example: in the dark, you can see the outline of a truck, but you can't tell if it's green, black, brown, red, etc. It's just dark. Same thing will happen to animals.
So like Venatic pointed out about blacklights, just like the IR cameras failing to pick up IR signature when an IR source isn't present, I'm not prone to believe that there's any reason to believe UV sensitive cameras, i.e. cat and dog eyes, won't pick up any UV signature if there isn't a UV spectrum present. Directly parallel, we see intra IR-UV light, if there isn't a light source, we can't see anything. I've played a bit with this and dark colored "near IR" color clothing and cattle, horses, goats, mules around the farm (which supposedly have IR vision beyond that of humans). In the dark or near dark, I can't tell any significant difference in them picking me up any different in clothing with high IR signature than any other clothes.
So I'm sure it doesn't hurt in the least, but I'm doubtful enough in the theory that I won't go very far out of my way to use detergent without brighteners. They're out there, but if I can't find the one I want (forget what we use, just know what the bottle looks like), I don't sweat using something else.
