The MEPs have none of their output leads grounded to the frame by design. Depending on the output configuration the earth ground and frame ground are attached to the specified output.
However, there is another scenario people should be aware of. The ground on the frame protects the user from shock if the user touches the frame of the machine when the machine has a short from the winding (or control panel) to the frame. The older the machine the more chance there is voltage leakage due to breakdown of the varnish used to insulate the windings. It is a given with age and there is no stopping it over time.
I test run and adjust my stuff all the time without grounding but I don't make a habit of turning wrenches on it while running. Operate it on a clean dry surface, wear good footwear and don't touch metal if not necessary.
I would not operate the machine ungrounded in wet conditions.
The machine itself does not care if it is grounded or not.