Yes they do, unless it is a purchase from Ebay/Bonz/private party where it's stated it is missing - possibly at the Rack or Outlet where it was sold "as is" final sale and was not shown with the bag.
Betty is a also one of my favorite bags - Enjoy your Betty!
I have heard that some of the bags from the outlets do NOT have the coin purse. I think these bags are made from surplus leather and therefore do not necessarily look exactly like the other bags that were in the stores. You have to ask before you buy if they have the coin purse. They SHOULD have them.