Technically, yes, I believe you're supposed to be licensed to buy a ham radio. I know some folks that bought theirs before getting licensed though.
Once you have your Basic license you can buy pretty much anything, though without Basic+ you can't operate on the High frequencies (HF).
You need to score 70/100 on your test to get VHF/UHF privileges, and 80/100 gets you HF as well.
People could figure out you don't have a license by the lack of a call sign. There's a lot of info you need to make sure you're not operating on the wrong frequencies, etc, so without the license ~(or having done a lot of the studying you'd need to GET the license) it's easy to make some pretty obvious mistakes.
The Canadian test is quite a bit more difficult than the US test, so there may be more very young hams in the States than in Canada. I'm sure we have some smart young licensed hams up North as well - they just had to work harder.
There's a wealth of Canadian-specific info at
Radio Amateurs of Canada