Engineering degrees will not help you become a pilot, at least in UK. In fact, in the UK there is little or no advantage in having a degree at all when it comes to obtaining employment as a pilot, though you may wish to have one to increase your employment prospects in case you fail to become a commercial pilot.
In the USA, on the other hand, a degree is required by almost all employers - though whether an engineering bias is preferred, I have no idea. I don't know about the Canadian system - perhaps someone here can enlighten us? I do know, however, that the Canadian commercial flying market is particularly small (for the size of the country), and overly dominated by the national carrier. Consequently, it's a very difficult field to break into unless you have military flying experience. Perhaps some Canadian-based pilots could expand on this?
That said, there's nothing particularly wrong with your plan (though you haven't said how you will fund it), but you will need to maintain flying currency while you're at university. Can you afford to do that? If not, you may wish to think about doing your degree first, then the flying training.
Scroggs