In Canada, the rate of all firearms deaths has decreased since firearms laws were tightened in 1993. I'm going by memory here, from what I remember from my restricted firearms safety textbook. However, the only real impact statistically in overall deaths was accidental deaths. People simply started killing themselves and others with knives and bludgeons. Sorry I don't have any hard numbers at hand.
I don't think it's a bad thing to have to pass a test that shows you know the basics of safe handling, storage and transport of firearms and ammunition, as well as the basics of the Firearms Act. There is a small fee to register for the exam. The written test takes about fifteen minutes, the practical test takes another half-hour or so. If you pass both parts with at least a mark of eighty percent, you have the written confirmation you need to apply for a Posession and Acquisition Licence.
Of course, this is no guarantee that people will observe the laws and use safe handling practices. Regulation will never eliminate foolishness and recklessness. I can think of several instances where individuals had passed the necessary exams and still acted irresponsibly around firearms, with death resulting in one case.
As far as the black market is concerned, handguns and the like are readily available for sale if you know the right folks to ask. You might have to look a little harder to find contraband weapons in Canada as compared to our southern neighbours, and they are far more expensive, but I'd imagine anyone who wants one can get one.