No, the job offer is not Employee Sponsor. It's just for the work permit.
Getting the number was really fast for me. It's an online process and they get the number directly after the payment goes through. First time I needed one was just after they changed the process and I didn't know. I was late with my application and got HR to take care of it on the evening of Dec 30 (my permit was valid until the 31st....). That only works when you're friends with the head of HR obviously, but just to give you an idea of how simple and fast it is.
If you can, ask them to save a PDF of the page where they verify all the data entered. You have to make sure you enter everything the same way. Especially make sure you get an end date to your job offer (even if they want to keep you for longer). Otherwise you may end up getting your permit refused, because the job offer "doesn't appear to be genuine". This happened to me because I got an offer for undetermined time, but I had to enter a date on the application form. So I put one 2 years in the future (max time for the permit is 2 years), and I got back the answer saying information entered by the employer and by the applicant wasn't the same and they didn't believe the offer was real. HR called and they got it fixed, but I was out of status for a week. Not fun. Avoid that
