1965 Dodge Dart Charger

Can it have been a test for different assembly lines for a period of time?

It's possible, though it doesn't seem like something that would warrant a cautious, slow, phased introduction. It's more likely the start date varied a little, plant by plant, just due to procurement factors.

Did they continue to use this plastic cover into the 70ies?

Yes.

Can it have been partnumbered later by Chrysler?

I've checked every US parts catalogue from '64 through '74, plus '82 through '89, plus the Canadian '66, and it does not seem to appear in any of them. I've also looked at a variety of vendors of the repro piece — sometimes an OE part number is given — but in this case, none. It just doesn't seem to appear in the parts catalogues at all.