Do the FUE dots tan in the sun? Or is it because they are scars they won't?

Scabs do not tan.  It is generally recommended that you avoid sun exposure after surgery.  If you're concerned contact your doctor.

The individual scars from the donor extraction sites won't tan because the scar tissue won't have the cells necessary to allow tanning to occur. I warn patients about this prior to the procedure. If the punch size is small and the extraction sites are distributed evenly and there is hair in between the sites, lack of tanning shouldnt be an issue because the above will camouflage the donor sites. I have recommended self-tanning lotion in the past for patients that get a dark tan in the donor area after the procedure has healed. That works well. 

it wont...Tanning may change the color of FUE scar but  it does not cause a normal skin color ad enough camouflage .