Ordinarily, it is not possible to edit Group membership from the Group admin because the m2m relationship is defined on User. With a custom form, it is possible to add a ModelMultipleChoiceField for this purpose. The trick is to populate the initial value for the form field and save the form data properly.
One of the gotchas I found was that the admin framework saves ModelForms with commit=False and uses the save_m2m method when the group is finally saved. In order to preserve this functionality, I wrap the save_m2m method when commit=False.