Be a waste of money in my opinion. A mini-cycle is cause by a loss of bacteria counts (new substrate, overambitious cleaning of the filter etc.). It also can be from the release of ammonia trapped in the substrate. BioSpira if kept properly adds bacteria to the tank but not in any great quantities. Remember a tank can lose up to 50% of it's bacteria and recover up to the previous numbers in one day. It can also take a sudden influx of twice the normal ammonia and nitrite and recover in the same amount of time. Your best bet with a minicycle is to just to do a few water changes to reduce ammonia and nitrite and let it pass. No need to dump more money into the tank.
Its "better" than cycle because it actually does contain some bacteria to kick-start a colony. However, it is not a miracle product in the sense that it will miraculously cycle your tank within a day or even a week. It takes more careful monitoring of your params than a simple fishless cycle...