For the most part, yes. Regardless of the condition of the battery, the alternator should have capacity to bring the battery terminal voltage to at least 13.5 or 13.8 at idle. By the time the engine gets to 2000 rpm, system voltage should be 14.2 or a bit higher. Even if the load is great, or the battery is really wimpy, at 2000 rpm, the alternator should be able to produce 90% or more of it's rated output; enough to raise system voltage above 14.0

Diagnosing an alternator that is draining a battery (it's rare these days but it does happen) is a little more involved.

Finding an alternator with a bad diode (or set of bad diodes) can be harder, a set of bad diodes would mean as much as 30% reduction in output - the alternator may not keep up at idle, but should at 2000 rpm.

But in the case of the two alternators that failed on me, they produced NO output - system voltage was around 11 with the engine running. That can't be if the alternator is producing current.