Pilot DAR has it right.
There is a lot of "terminology" splitting hairs here, the sort of thing which the exam writers love
An alternator, with its voltage regulator, is a constant voltage power supply.
Unfortunately, while (with a sophisticated voltage regulator) it could work by itself, most current implementations do rely on the presence of a battery for stability and a smooth output voltage. The alternator generates a 3-phase output which even when full-wave rectified still has a lot of ripple on it and would play havoc with a lot of avionics, if the battery was disconnected.
If the alternator, or its rectifier, or its voltage regulator, fails then you are running from the battery until it goes flat.
Unless the voltage regulator fails into a short in which case the thing will run until the battery overcharges
The only alternator system I know of which can run with a smooth output without a battery is the GAMI Supplenator but that does't "exist" yet.