Yes! The best method for indexing your YouTube videos (or other streaming video content) is to have each video embedded within their own pages on your site.
Swiftype will not crawl and index the actual video file embedded on your site, but will index the hosting page. This means you can add additional context for the video (description, tags, etc) to the landing page and allow your visitors to query those terms within your site search engine.
A significant benefit to setting up your videos on your site this way is that it will keep your visitor traffic on your site without sending it away to YouTube or another video streaming service.