I am just curious what will happen to a series wired HID ballast such as a 6.6a series mercury ballast if it is wired to a parallel circuit such as a 120v, 277v, or a 480v supply?

The "series ballast" is just a transformer turninh the 6.6A into e.g. 1.5A for a 175W lamp.
It does not exhibit any significant internal impedance, as the series circuit is already a current source.
But when you connect it to a voltage source (e.g. 27V corresponding to the example setup), you get a constant voltage secondary, with no ballasting whatsoever.

The thing is, while incandescents dont care if they are fed from high impedance constant current or low impedance constant voltage source, the discharges needs exclusively a high impedance constant current source.
The series circuit is already like that, so only the current value transformation is necessary for the lamp. Or if the lamp current would happen to match the circuit current, the lamp could be connected just directly (assume you shenenigans like lamp failures or hot restart and so on).
But when you want to operate the discharge from a constant voltage source, the ballast function is, beside eventual OCV transformation, to provide the high impedance so the lamp will see again the constant current source.
The transformer just whatever source impedance to the secondary, but does not change the nature of that impedance. So when connected to a low impedance source, the secondary will act as a low impedance source too. And when the same transformer connected to a high impedance source, the secondary will act as a high impedance too.