If you use the method shown in the video, you CAN'T get back to the original multi-take Region after comping -- you would have to use the method I described [keeping/muting the extra Take tracks], NOT the method shown in the video, if you want to be able to go back after the fact and change the Comp. And even with my suggested method, apparently you still can't make a cut-up Take into one long Region again after you've cut it up, though you can retain & reuse all the pieces of each individual Take if you've *Copied* the desired sections to the Comp track and kept all the individual pieces of all the Take tracks.
As I said, Comping is not fully [& conveniently] implemented in GarageBand, as it is in Logic and other DAWs -- you can either fake it with the approach I suggested, or upgrade to a real DAW [if that feature is critical to your workflow].
Command-J is really meant to join different segments of audio into one new file, but since the method of comping shown in the video seems to strip away the references to the extra data [or audio] in a multi-take Region after you cut it up, I'd guess that's why it's not going to do what you want it to -- in fact, it doesn't seem to work at all with edited multi-take recordings [MIDI or audio], so forget about it for this application..