depends on the type of the pill
from my experience, the pills that make your hair less curly are the ones with estrogen - nearly all of them. Most pills today contain estrogen+progresteron.
Estrogen might cause high colesterol and trigliceride levels, to the point that it's unhealthy. that's what happened to me.
So my doctor switched me to a pill which contains only progresteron. it's less recommended, because it makes your period irregular. for me, it was first 2 months of constant but very minor bleeding, and since then - nothing. But I guess it's different for every girl. This pill is also recommended for women who are breastfeeding, by the way..
I was VERY happy with my hair a bit less curly, it made it very beautiful.. but I can't really go back on those pills. But I see that most girls here are unhappy with that, so you should ask your doctor about estrogen-free pills.
Also - this is the only place I've ever found a reference to this subject, so thanks!! I thought I must be crazy to think that..