Not the case at all. Just because someone doesn't physically sign “an oath”, doesn't preclude them from the responsibilities of their office, nor does it EXEMPT them from accountability for violating the terms of that office. The minute they perform ANY official act as an officeholder, signed oath or not, they are legally bound to perform all of the fiduciary responsibilities of that office, as well as the ramifications for violating those responsibilities, including illegal acts, To include treason.

Don't think for one second they can make that bullshit “I didn't sign anything” excuse/argument with any success. No jury/tribunal will give a fuck about the lack of a signature as a get out of jail/gallows free card.