Along the same lines, if you have a product that is Class I with a plastic enclosure, does it need a ground stud?
Assuming that you are thinking of an external ground stud, then I would suggest that, no you do not have to have one.
However, electrical equipment, especially medical devices, are routinely tested often by a hospitals own engineering / equipment management service. A key test that they will try to do is earth bond integrity. If they cannot find a suitable earth point they may attempt to use something like the metal shell of a connector. As this test is usually done with 25 amps of current it would likely cause damage if that current was passed through unsuitable conductors, such as a PCB trace.
But if you provide an external earth point, with strong bonding then the test is easy to complete and no damage is caused.
As with just about everything in this game it's all down to risk analysis.