A quick look around says commercially available bill counters count around 1000 bills per minute. Low cost counters have batch sizes of around 200 bills. Larger capacity counters are available.
Assuming the process keeps a single counter running continuously, it would be 1000 minutes, not quite 17 hours of work to do a single pass counting with one counter. There's a maintenance interval though. Some of the counters will scan serial numbers, so you could probably confirm you saw 1 Million distinct serial numbers while scanning. Multiple counters in parallel would reduce the wall clock time, of course. And you might want to do multiple counts, sometimes bills stick.
You could also count the number of straps and take a random sample to count. While counting the straps, you'd probably notice any grossly miscounted straps. If any of the sampled straps are wrong, you would presumably increase the sample rate to confirm. Weighing groups of 10 straps is probably faster than counting, but I don't know how sensitive it would be (depends on how consistent weights of the strapping material is, as well as weight of circulated bills).
