I know there were some free applications out there that could extract the source file... as long as it is in a format that the Movie Edit Pro can handle then yes...
I have used the screen capture in Movie Edit Pro to do this.
This is a screen shot from the Movie Edit Pro 17 Plus...
If you use Mozilla Firefox you can download 'Download Helper' which is a fantastic free plugin, it will download almost all video's from You Tube and other similar sites as flv files, you will need to convert into a format Magix will recognise before importing or you can buy 'Download Helper' for a small fee and it will do the conversions for you. It also works with Internet Explorer but was originally written for Firefox. I have not found Magix products reliable enought for streaming video's, its a bit hit and miss whether the end product will turn out right, the settings seem to change of their own accord so I use 'Applian Director' then import into Magix for editing. There are other products out there both free and to buy for downloading You Tube video's, another good one is a product of AShampoo's but for me and I recommend 'Download Helper'.