I did some more investigation, and found this on the Eaton web site:
Q: I’ve decided I need to change the oil in my supercharger. How do I do this?
A: If you do want to change the oil there is one fill/drain plug on the front face of the front cover. It will probably be an Allen type plug. You will have to suction out the oil using a syringe or other method before replacing with new oil. Fill levels are dependent on application. For aftermarket units, please consult the aftermarket partner company that produced that specific kit. For OEM units, please see the list below or email
[email protected]. New oil can be obtained from any GM or Ford service parts facility, or from one of the Eaton aftermarket supercharger partner companies or remanufacturers. Please make sure you do NOT use any other type of oil, including synthetic motor oils. These will cause failure.
So there is an oil reservoir, not a pressure feed from the engine, as I had thought. But note the warning about using the wrong oil, especially synthetics. I know that those often are bad for gearboxes, so am not entirely surprised.