It's kind of a goofy thing. There's nothing on the ATT conditions any longer that says you have to have the registration certificate with you (At least on mine, licensed in January, for transport within my home province of AB), and one agent I spoke to said as a result of it not being listed, you no longer have to carry it with you when you go to the range, but have to have received it in the mail before taking the restricted pistol out to the range. Ergo, yet another legal Shrodengers Cat if you were to get pulled over with a recently acquired firearm, without the reg. How would they know if you've received it or not?
So you're probably fine in theory to take it out with only the transfer letter, but it could be seized if a peace officer feels frosty, and then you'll have to go get it back once the certificate does arrive, which I imagine wouldn't be a great experience. Chances are most officers are going to follow and enforce the old rule of having to possess the certificate during transport, so you'll save a lot of hassle by waiting.