Youtube Logo by Rego Korosi (cc) creative commons 2.0 - https://www.flickr.com/photos/korosirego/4481461680
No. Youtube videos can only be used for personal use, in a non commercial context.
Youtube's current terms say you may:
"use the Service to view or listen to Content other than for personal, non-commercial use (for example, you may not publicly screen videos or stream music from the Service); or"
For more information, please see Youtube's terms and conditions
If you have any specific questions about copyright at MIT, please email Bernard Lyons, Copyright Officer