Yes, easily. There are three ways to put a YouTube video on a WP.com blog, covered in the Support and FAQ, but the one which simply ALWAYS works is the shortcode method:
Copy the URL of the video from the “More” box on the side. Then in the blog post: [youtube=URL] and that’s it. Some themes make you do it from the HTML editor, but most will accept that shortcode in the Visual editor, and you can use the column buttons for alignment.