"Would tapwater also help terminate fungal gnats while plants are young and vulnerable?"

That's a good question.
Got no gnats here.
(yeah dryer sheets!)
But someone who does, can test this easily.

All you need is a scoop of soil infested with larvae.
A small bowl, and some tap water.

Put the scoop in the bowl, whip out your loupe, and look.
Got wrigglers?
Add some fresh tap water, wait a couple hours, look again.

Be a good idea to just leave it and check every 8 hours or so for a few days too.
(If the Chloromine does not kill them outright but does affect their digestive process, it may take a while.)

Now ya know.

Tell us what ya find and we'll all be a tiny bit wiser.

Aloha,
Weeze