You do need a license, it's just easier to get, since there's no Morse Code test.
The first test is the Basic, and you can pass either at the 70% level or the "honours" 80% level. Honours lets you operate below 30 MHz. Non-honours restricts you to VHF and above.
Basic holders may operate cross-band repeaters, and same-band store-and-forward repeaters. That's clarified in an FAQ on Industry Canada's website.
There is an option to take a Morse test, at 5 words per minute, and if you pass (and if you've also passed the Basic), it grants you the same privileges as getting honours on the basic: i.e., operation below 30 MHz.
The other license class is Advanced, which allows higher power on some bands, the right to build your own equipment, to install club equipment, and to operate same-band repeaters. It also grants the right to the whole Amateur spectrum, in case you hadn't previously gotten your Honours and/or 5 w.p.m.
In no event does your license class restrict what operating mode you use, within the bands you're entitled to. And Canadian bandplans don't reference license class, either. So you can try Morse even if you've never passed the Morse test.
It's been clarified that only Advanced license holders are eligible for the CEPT certificate that allows operation while visiting certain EU countries. This is not because of the Morse, since dropping the Morse requirement is ITU-wide. It's some other element of the Advanced curriculum they're after.