With where we are in our Epicor journey I think it is time for me to consider copying our LIVE database onto our THIRD/Test environment, however I am curious will I need to backup all the customizations to get them back into the THIRD/Test database or do they get migrated along with the database or left behind on THIRD and not impacted by the database copy process?
They should be copied over. They are all stored in the dB.
Yes, just make sure to export out any WIP customizations you are working on and want to save/keep out of Pilot/Third first. Been burned by that before.
Burnt myself on this a month ago, had backups of test luckily haha.