Dilation question

An
If I start effacing, does dilation happen soon after? I have no idea how effaced I am but at my 38 week appointment today my doctor said baby has dropped finally and that my cervix is "softening up and becoming shorter." I would like to get my membranes stripped next week but obviously can't if I'm not dilated. With baby Being dropped, does dilation just naturally happen? I think I read that dilation occurs when the baby drops lower into the pelvis. I'm not trying to rush her out but I am trying to avoid induction as this is my first baby. Hope these aren't silly questions!