They shall in all Cases, except Treason, Felony and Breach of the Peace, be privileged from Arrest during their Attendance at the Session of their respective Houses, and in going to and returning from the same; and for any Speech or Debate in either House, they shall not be questioned in any other Place.
Like I said to another poster...IMHO, it may make for an interesting constitutional challenge, but it does not change the facts about what happened, his pleading guilty to it, or his judgement regarding it.
It may clear him technically on a legal basis, but it does not change the fact that it happened and his actions regarding it. That is the essence of why, IMHO, he should resign.