Is a separate safety earth connection necessary when using an earthed power entry module?
the problem is that raw aluminum quickly forms an aluminum-oxide coating which is insulating. This is the reason for the recommended ground connection with a toothed washer to cut through the oxide coating and contact the metal.

The module appears to have a plastic front through which the screws go so the mounting screws will not provide a ground path, even with a toothed washer. The incidental contact of the module body to the edges of the opening will not prevent formation or break through the oxide layer so there will not be a good ground connection.

To ground the aluminum chassis, I highly recommend following the diagram.