oh i use that dye all the time and it never damages whatsoever
in fact, my hair looks 100 times better/feels better once i color it!
im sure it would be fine since its just a semipermanant dye.

and this isnt that related to your frizz thing but a note on the haircolor, i bought nutmeg because my hair is close enough to that and i left it on for like 5 minutes too long and my hair turend BLACK so be careful, you really only need to leave the dye on for what they say on the box!
good luck!