UV Red coolant does not exist. All UV red coolants are red dye with UV pink dye, and the color pigment achieved depends on how much red dye / UV pink dye used. The more UV pink you use the more it will glow, but the pinker it will be when UV light is used. Finding the right balance can be difficult.
UV reactive means the color pigment glows. There is no universal UV reactive dye that will make the color it's added to glow. Clear UV glows blue when 3xposed to UV light, so to answer your question no, clear uv with red dye will not make it glow UV red. It would make it an off red/purple color when exposed to UV light.
What's the specific color theme of your build?
If it's black/red you could go UV red tubing, with a pastel black coolant so that your reservoir, transparent waterblocks, etc. will be black, but the tubing will be UV red.