Car alternator

So on my Honda Pilot, I have noticed struggles with start
about 3-4 weeks ago. Towards recent, the car struggled to
start more often. The "struggle" was that the starter would
spin normally, but the engine "coughed" several times
before starting.
Recently, I tried unlocking the car, but the remote wouldn't
work since the battery was dead. After cleaning the
terminals with baking soda (they were all corroded), I
jumpstarted the car, and it started normally. Within 1-1.5
hours, turned off the car, and the next time it started
normally (the alternated did its job just fine).
Now the car is at a service, and they're suggesting they
should change the alternator. So the question is: could the
alternator go bad and drain battery once, but then operate
normally right after? Or is it probably something good else?