Yes, they do, in a confusing manner. The factory radio has a small powered display on it and has to be illuminated. There is a radio illumination relay for this purpose. The relay works in such a way that when you flip the key, battery power runs through the relay to the radio to power the radio screen at full brightness for daytime viewing. When you turn the parking lamps on, the relay switches the radio to where it gets voltage from the orange dash light wire, which is dimmable, so the radio screen can be dimmed at night with the rest of the dash.
You can ditch the orange dimmer wire, or you can hook it up to your stereo if the stereo is auto dimmable or if you're switching to a different radio that has that function. So like in my jeep, I use a sony, and the sony is dimmable. So I hooked the orange factory dimmer wire (same as dash wire) up to my radio. When the parking lights are on, that wire has voltage, and the radio sees it and dims itself. That radio will dim anywhere from 0.1V to 12V. So actually when I roll the roller down to nothing, the dash circuit has 0V, the radio sees no more voltage, and goes back to full brightness. This is great for rainy days when you want your headlights on, but still want the radio to be at full brightness and don't want your gauge backlights on.
But back to your question, yes the dash light wire goes to the radio itself and to the radio illumination relay.
The radio actually has two power inputs from the dash, one from the relay, and one directly from the dash lights. The one direct to the dash lights (orange) is for the radio buttons to power them (dimmable). the relay output is for the screen specifically, so that it can be full brightness when lights are off and dimmable brightness when lights are on. the buttons don't need that functionality because they are labeled white and have full visibility during the day when they're off.
Sorry, not trying to write you a novel here, but I figure the more info I can provide you, the easier it will be for you to make sense of what you find in your dash, what it's original purpose was, and what you can either delete or repurpose for a new radio if you want to buy one.