Whether a cd will play in a dvd player really depends on the brand of player; however, there can be no doubt that burning files to an actual dvd will get you better results.
I know my Philips dvd player will play all kinds of media and files and you can watch straight .avi files on a dvd (or even off a hard drive) without converting them to dvd format, but that is not the usual case. Most dvd players only like to play actual dvds.
If your player is like that you can use a freeware program like DVD Flick to author the dvds. It is very easy. Whether the youtube videos are mp4 format or flv format, DVD Flick will automatically convert them and author the dvd and then you can set it up to automatically make an image file and burn the dvd as well. It's a great program and I'm actually using it right now to author a dvd that a program that costs money to use refuses to do correctly.
If you don't have a dvd burner, then you are out of luck and I suggest you get at least an external dvd burner for your computer because they are cheap and will make your life better!