Can you put a curly perm in hair that previously had a straightener?

I'm growing out my straightener and I naturally have very curly hair so the two textures aren't nice. I roll my hair after I wash it to make my straight hair appear curly but, could I just get a curly perm to put on my straight ends that way my curly hair would look natural when it grew in instead of having 2 textures? Or, would this be too damaging?