as far as I know the guide you linked has been written with a generic WebCenter Sites environment in mind, I do not think that it makes a distinction between delivery and management sites instances. I can understand that is not ideal but customers can perform cold backups of delivery during scheduled maintenance windows .
I am not aware of existing issues with customers performing hot-backups while the site is being accessed. But it is most likely something that has not been intensively tested, unexpected side effects could still happen.
I can see how the DB could be under stress during the backup process and this could have in turn a detrimental effect on the performances of Sites. At the very least you should make sure that there are no publishing jobs scheduled when the backup is supposed to run, and if possible make it run during low traffic hours .
Thanks for the reply, Pietro.
Yes, the backup will be done while there's no publishing being done i.e. Authoring app server will be down, but delivery app server will be up. Also, the backup will be down during low user traffic.
I just wanted to ensure there are no adverse functional implications or data inconsistencies if a hot backup was taken of the Delivery database and filesystem, while the system was up and running.
It sounds like there are no issues, apart from a slight performance degradation, which is expected.