The TSA locks work and will not be cut off if they are operational. We've had a couple problems with TSA and sticky locks.
Unfortunately, because locks are hard to cut through, TSA tends to cut the zipper loop on the bag if they can't access the lock. Which leaves you with a damaged bag. For this reason, we only lock bags that have Scuba or other equipment and then we inventory the bags at the airport if the red dot on the lock tells us the bag was opened.