we do those moves all day long in the sand rinse thread without bac, moving the rock moves the entire biofilter, even if you removed all the sand or replaced it during the move. adding bac wont hurt, def don't buy any. we wouldn't even use it in my sand rinse thread/tank upgrade thread
the most important part of your move is how you prep the new tank using the old surfaces; none should bring in clouding. old / used live rocks have retentive waste; rinse that out by shaking rocks in a bucket of clean saltwater or some other creative way of cleaning them / no detritus before setting back up in the new tank.
even if you add new sand, and more fish, your current rock handles the move just fine we've been doing this for 30 pages yep. live rock simply supports much more bioload than what its used to, its not true that it requires more bacteria, its always in excess. thats one of the reasons people can have a bunch of fish, one dies wedged in the rocks, and the tank doesnt crash. even bioload+extra instant rot before buildup wont crash the tank, it absorbs all that extra load ammonia.