Up to roughly 100 bills it's pretty much bang on - even with a cheap $10 scale (American Weigh Scales Digital Pocket Scale has a bunch of different options). Each bill weights roughly 1 gram. So - accurate to within 1% - and presumably the banks have better scales.
I suspect at scale (moving either a lot of batches or large batches), you also need to take variance into account more. Some bills might be dirty or have stuff stuck to them, some bills might be damaged and have bits missing? And other things that occur in practice that I can't think of from the comfort of my armchair in 30s.
It wasn't very precise but you could move a lot of money in ball park with this method. Atleast internally across branches.