Yes, you can. You click 'Embed' on YouTube, extract out the URL from the src="..." tag, then click the Flash button in Q2A's rich text editor and paste in the URL. Example:
Welcome to the Q&A site for Question2Answer.
If you have a question about Q2A, please ask in English.
To report a bug, please create a new issue on Github or ask a question here with the bug tag.
If you just want to try Q2A, please use the demo site.
May 7, 2020: Q2A 1.8.4 released!