I'm not so sure about that. As I understand it, the requirement for Class II require that there is adequate (double or 'reinforced') insulation between 'live parts' and the outside world - so I'm not sure that would theoretically preclude electrical connection of some outer conductive part (outside of the insulation) being electrically connected to something which was not 'live' during normal operation.Surely that is an oxymoron. Even if it were alowed, it could hardly be described as Class II. I.e with no insulation.
However, you're pursuing something which I only wrote 'as an aside'. My primary point was that, in relation to the suggestion that filter capacitoirs might be connected from L and N to the unearthed casing of a Class II item, that is something which I have (a) never seen, (b) never heard of, (c) not been able to think of a reason for and (d) am not sure that it would even be allowed. As the 'aside', I merely added that, as a generalisation, one does not expect (maybe 'not allowed'?) anything (whether a filter capacitor or anything else) to be (electrically) connected to the unearthed casing of a Class II item.
Kind Regards, John