i am happy to try and help when i can 
one of the other things that clonezilla can do is create an image of the partition you are interested in having as a backup. an advantage of the image over a clone or copy like the one i believe you have created is that there is some compression involved so it takes up less space. after my backup in january, i compared the space used on my hdd and what was taken up by the image created by clonezilla. the exact numbers are listed in the first link below, but there was a greater than 50% compression rate which is helpful for (possibly over-) cautious folks like myself who keep a few backups just in case the most recent has an issue.
i have read before (and there is a post in this forum [second link below]) that it is possible to mount one of these images to get access to individual files. i haven’t tried that process yet, but it is definitely on my list of interesting possibilities to play with one of these days.
to answer what i believe is the main point of your question: yes. i will use my copy process to try and explain why that is a qualified yes at least in my case.
when i used gparted to copy from my internal hdd to my external hdd, i chose to copy my third partition which has debian installed on it. i copied debian to the second partition on my external hdd (the first is where i keep timeshift snapshots/backups). running sudo update-grub locates that (hopefully) valid, bootable partition on the external drive and adds it as a boot option on the initial grub os choice screen.
the reason my answer in my case is a qualified yes is because of the placement of the partitions i chose to copy and paste to. if (in the admittedly very minor possibility case) i had chosen to copy my third internal partition to the first partition on the external drive and then i wanted to take that external drive (mine is a bare hdd in an enclosure) and put it in my laptop and use it as an internal drive, there would be no grub (no bootloader at all) to tell the system to load the os even though it is valid and bootable.
i do not know for certain (i don’t have an extra drive to test the possibility) that this would result in the os not loading. perhaps your suggestion of adding the boot flag with gparted will allow it to do so. i just wanted to add that there is a possibility in this particular case that things might not go as planned.
what i understand of your process so far leads me to believe that you would probably be able to boot a drive where you copied the first partition (grub is generally written to the beginning of the drive [though this can apparently be changed] when installing most linux distros) to an external drive and then installed that drive and used it internally. i again say “probably” and hedge my bets because the only time i have used clonezilla to perform a complete restore from a backup image was onto the same disk (i messed something up with an update) the image was written from. i have not yet had the need to restore a backup image to an entirely new disk because of disk failure. theoretically that is exactly part of what clonezilla was designed to do. i just haven’t tested that particular function.
i hope that’s not too many if’s, and’s, but’s or wall of text imposing in general the reason i use a couple of different backup methods (timeshift and clonezilla as well as smartcontrol/smartd in the background) is because i just want to make doubly (and possibly triply) certain that if i do lose a disk there is some hope of recovering my more recent work.