It will likely take a couple weeks total.
I'm not sure how the timetable quite works out. I believe once the vertical portion and prep for the horizontal is drilled, they have some cement work to do. If that is about the same as a regular well, that will have to cure for 5 days, give or take.
I've heard that it will take a couple weeks to drill the horizontal well, but I don't know if that 2 weeks includes that cement curing time or not.