About to be a first time mom, Ill be 37 weeks on Wednesday and obviously I am very, very anxious to…

About to be a first time mom, Ill be 37 weeks on Wednesday and obviously I am very, very anxious to meet my son! I havent noticed the loss of my mucus plug yet but tomorrow at my OB appointment my ARNP and I have discussed the start of thinning my cervix/stripping the membrane, which after that if your cervix has already began thinning could take 2-3 days for labor to start and I am still working full time, walking and on my feet for 8+ hours a day. That being said, do you have to have lost your mucus plug for your cervix to have started to thin naturally?