All Miami students have YouTube accounts through their miamioh.edu credentials that provide access to higher-level features; it’s provided to them (and everyone with a @miamioh.edu account) via our Google Apps for Education account. So yes, students can upload videos to YouTube, then paste links for them in an assignment or discussion in Canvas.
However, you’ll want to make sure that students understand YouTube video privacy settings so their coursework isn’t publicly available on the web without them knowing it.
YouTube has a handy guide on how to upload videos that includes both text and video instructions. You could share it with your students if they’ll be sharing videos via YouTube for one of your course assignments.