http://www.transportation.alberta.ca/1951.htm - You can drive for 14 days with the old plate on the new vehicle before you have to transfer the registration, but you shouldn't be driving the vehicle at all without valid insurance.
As others have said, if you buy from a dealership, they shouldn't give you the keys without seeing proof of insurance (I think my insurance company faxed the temporary pink slip directly to the dealership when I bought my current vehicle). If it was a private sale, the other guy isn't going to care what you do with it once he has his money.
Like you said, she probably wouldn't have noticed you if hadn't been struggling, but suspicious behaviour is what makes the cops suspicious.
At least you didn't run from the cops (not that you could have if you kept stalling) like that guy the other day who plowed into the house and died in a fiery wreck, just because the cops happened to run the plates and noticed that the vehicle was registered to an older woman (his mother) but was occupied by 2 younger men at 1:30 in the morning.