Effects of a body tattoo that looks like a tan by UV rays?

This question initially sounds ridiculous, but hear me out.

It’s not at all uncommon for cosmetic surgeons to tattoo eyeliner or lipcolor, so I wonder if a tattoo artist would consider tattooing a tan on someone. Yes it’s ridiculous, and it’s much easier and less painless to get a suntan, but I’ve seen several programs on TLC and Discovery where someone was tattooed over their whole body. Which leads to question…

Would you be less likely to sunburn? Would the pigment reflect the UV rays or keep them from penetrating too deeply to cause cancerous growths? Would the pigment absorb heat, radiation or UV rays and make sunlight more dangerous?
Are there areas on the face where you can’t receive a tattoo? If they do lips and eyelids it seems like no place is off limits.

If you attempted to suntan, or even allowed yourself to burn, your “tan tattoo” would fade quite quickly. Ask any tattoo artist, and they will tell you that sun exposure on a tattoo is one of the quickest ways to fade it (setting aside improper care during the healing process). And tattoos just fade naturally over time anyway, so it wouldn’t be much more permanent than regular tanning.