Well another comment sites a specific property that chameleon alone gives 20% - So who is right here?:

Your second paragraph has the answer;

ench_mod_LegendaryArmor_Chameleon and what it does is give a Stealth Field magnitude of 20, which is 20%, and multiple pieces do stack.

The field while active, gives 20% to sneak. The ingame presentation is the invisibility, but it's really just 20% more sneak while stationary, code-wise.

Let me rephrase my second question here: Does Stealth (Field) serve any purpose other than detection avoidance?

None. Other than make it really hard to read the pip boy ;)

it sounds like all that Chameleon does is it makes you undetectable when still and sneaking, but it has no effect after an enemy has already identified you.

Correct, mostly. It won't make you undetectable either. It's really just a 20% to sneak while stationary. The visuals etc. in game don't matter.

Enemies will more quickly go from stages if they're searching for you and such, while it's active, as it's essentially 20% 'more' sneak, but if they are aware of you though, it won't make them not see you and stop shooting. If you run and hide, and sit still, they will drop aggro faster if they can't find you, as it's again, 20% to sneak while on.

So if sneak rank 5 put you at say, 100%, sitting still with chameleon is like having 120% basically, but only while still.