I was told the Notice of Transfer only allows you to take it home because you must have the actual registration card for the firearm to transport it anywhere else.
Prior to C42, there were quite a few discussion here about the requirement to carry the registration, with considerable disagreement.
With the prior ATT system, some provinces had it as a specific condition on the ATT that you had to have the registration.
That left no room for doubt. You required it, if your ATT said so.
Some provinces did not have that condition.
As far as I am aware, the post C42 country wide wording doesn't have it as a requirement.
Then, now as before, we are left with the Criminal Code (because the firearm's act says nothing on the subject).
I won't give a long quote, but sections 95 & 117 are relevant. [Read them yourselves. This isn't legal advice]
In a nutshell, section 95 says you need to be able to produce it on demand and be the "holder of".
Section 117 says if you can't produce it, they can seize the firearms and you have 14 days to produce it.
After 14 days, it goes to court.
So IF the LEO accepts the other documentation you have (transfer, etc.), then you would be OK.
There was also debate about the wording "holder" of a registration certificate, and whether that requires physical paper, or that it was registered and on file.
So, waiting for it is the route of least hassle.
Not having it isn't an automatic go to jail though, especially if it is expected in the mail within 14 days.