No. If your friends and family are in the same room as you, they can watch the ceremony with you. However, you can't record or broadcast the screen.Question to those who have done the oath ceremony.. Can it be broadcast so family overseas can watch?
IRCC was/is considering this option but it isn't available yet because of "technical limitations" (or something on those lines). I found this discussion buried somewhere in the 353 page corporate records document that I obtained via an ATIP request.
https://drive.google.com/file/d/1uLTJFxlUwXj3YHpXrcvMITBf9YbLbF6s/view?usp=sharing