No it was not supplied by the alternator "exactly. Originally, because of the ammeter, and the need for it to be able to display current flow either from or to the battery (discharge vs charge) BOTH the battery an alternator wiring had to appear at the ammeter. It's all one wire. Here is an article about repairing bad bulkhead connections, but in this case what you are looking at is the simplified power distribution diagram.
Follow along in the diagram. This is a simplified diagram of pretty much original OEM. Bear in mind that the ammeter is basically a "piece of wire". So the RED wire shown starts out at the battery, goes to the starter relay "big stud" which is part of the relay contact, BUT ACTS AS A JUNCTION point. From there to the fuse link, then through the bulkhead connector an to the AMMETER, through it an out on the BLACK wire an to the WELDED SPLICE. This splice is up near the cluster a few inches from the ammeter. The BLACK continues on out through the bulkhead and to the alternator
LOOK AT the welded splice. This is simply a branch, tap, take off point. The battery and alternator ARE CONNECTED SIMPLY by the path just described.
The "WELDED SPLICE" taps off to the various points shown AND IS SUPPLIED by whichever is more positive........the battery....or the alternator. If the alternator is charging, and outputting more voltage than the battery, then the power comes from the alternator. If the alternator is not spinning fast enough, or the engine not running, then power comes from the battery.
Catalog
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The big question for you is, "are you going to retain the ammeter" because if you are, it's a fair amount of extra wiring with LARGE wire (needs to be upgrade from OEM) an the ammeter itself can give trouble with high output alternators. Frankly I would eliminate it an replace it with a voltmeter