No. Many people are able to book visits with their family doctor (GP) on short notice (e.g. next week). Walk-in clinics are available and you can see a doctor within a couple hours, same-day, without an appointment (and without being registered beforehand, literally just walk in). These doctors are fully licensed.
Although it's not easy to find a good doctor that you like, there are family doctors available for new patients even in busy cities like Toronto. Specialists might take a while to book (assuming it's not serious). Emergency rooms are always available (although you may have to wait a few hours if it's not really time-sensitive). Labs can be booked same day and may have a bit of a line up but you can get those for free too (for most types of tests).