Agoda bookings are accepted. After confirming the booking with Agoda the hotel will contact you and ask for a few things to complete the registration and then they will send you the reservation page that you can submit for Evisa or Thailand pass. I haven't seen any Bookings.com being accepted. Go with Agoda if you don't want to deal with the hotel directly.
Mine took 7 days. Applying from Canada. If you are from one of these countries and have everything in order then it's pretty much approved immediately.