Testing your film speed in itself is not a simplified version of the zone system. While it is part of making use of the zone system, the point is to determine what the the film speed is given your equipment, metering technique, and processing methods/chemistry, since that is different than what the manufacturer used to determine the speed.
Once you know the proper speed for your equipment and methods, you can make use of the rest of the zone system or not. But having done it you should achieve more consistency in your exposures.
To answer your other question, yes, once you determine that film x is speed y, then you set your meter to speed y, regardless of what the box says, as long as you're using the same film, developer and methods you used to determine the speed in the first place.