This is exactly what I have been told also by the Canadian Firearms Program when I have called them in the past. I wanted to play it safe, and requested an ATT for my pistol that I could take with me, and they told me I already have one. The registration number is the same on the confirmation as ton the Registration certificate.
All this said, it occurred to me that there are enough questions here at GOC and CGNs, and the unlicensed cops would be even less informed; I have always just waited that couple days to a couple weeks until it arrives; it's not like I have nothing else to shoot.
I just got a new GP100 private sale from AB to Ont. Transfer took 5 weeks; the gun was 6 1/2 days in transit, 9 Business days for the Cert. to arrive. I have not shot it yet as I have not had time to load ammo... I've had brass, powder, dies and primers for some time; bullets for a week and a half, shell plate for my press for a week: Tomorrows job. LOL.