It should.

You can tell by actually opening the user folder and see what's in it. You will notice that it also copies your desktop exactly how it is. If you get info on your user folder, you will see that it's almost as big as your HD. Well, given you only have one user and you didn't installed any apps that take up like 50 Gigs.

Don't erase your iMac until you verify everything you need is on your external. That is something I highly recommend no matter what method you choose.