Membrane Sweep?

I'm 37+5 today and I had an appointment yesterday. My doctor said that he would check my cervix and if I wanted to, he would do a membrane sweep to get things going at my next appointment if it looks like I'm not making any progress. I'll be 38+4 at my next appointment. I'm just wondering if I do get it done what kind of results should I expect? If you've ever had one how soon after did you have your baby? I'm all for anything to get her here faster!