This may be a little bit late (maybe!!) lol
I had mine done when I was 3 days overdue, and caused so much trauma that I was actually admitted to the ward about 20mins after because of the sheer amount and force with which I was bleeding. It was the most painful experience - and prompted me, along with outher previous encounters, to make a formal complaint about the doctor involved.
Anyway, I didnt go into labour until I was 7 days overdue! lol so no, It doesnt always result in labour.
And no, the bleeding and mucous may not be your 'plug' either, or not enough of it to make a difference.
I had another done after I had been in labour for about 27 hours by a midwife and I dont know if that one helped or not because 2 hours later I was in the OR

So I hope your bubba is on the way, but dont be too surprised if the little man still comes when he is good and ready, no matter how many people poke his head! lol
I wish you all the best for a safe and happy arrival of your young one