Sperm contains natural prostoglandins which can help soften the cervix, however, if your body is not ready to start preparing for birth it's not going to help. I've used KY or the store brand of it with all my pregnancies. We've also continued to engage in intercourse up until delivery with all of them. I don't know if it helped or didn't but I really don't think the KY hindered it in anyway. Aside from my first being an emergency c-section. My next 3 were born atleast 4 days before their due dates. My last I was induced on my due date. What *I* feel helped me with my pregnancies was walking. With the 3 that I delivered before the due date I walked atleast 5 days a week in the last 2 months. With my last one where I was induced I was working full time at a sedentary job and didn't get any exercise. Not sure if this helps you or if I'm just rambling...sorry.
I am not sure about this... We use a product that is safe for couples trying to conceive and I also have some KY but have not used it just because I figured that if it wasn't ok to use while TTC then I didn't want to use it when I was pregnant. I think that it could block the sperm softening the cervix though but I am not 100% sure. You can always ask your doctor =)