The post you are replying to obviously means the "electric chair," not a committee chair. Besides, the only upper house of a legislature that Snowden would have any chance at is more properly called the "Federation Council of Russia," not the Senate. Snowden is singularly unsuitable for any office of trust in the United States, and it is inconceivable that any American political party having a majority of the US Senate would appoint him.
Congressional Research Service: "Once a person meets the three constitutional qualifications of age, citizenship and inhabitancy in the State when elected, that person, if duly elected, is constitutionally “qualified” to serve in Congress, even if a convicted felon."
Also given that U.S. Senators are about the only people who can get off the "no fly list" because of their special status as senators, being a senator would probably excuse pretty much and current or past conduct by Snowden, just as it excused past conduct by Sen. Roderick Wright (8 felony convictions, set aside for prosecutorial misconduct; too bad Aaron Swartz didn't have the same judge).
FWIW, Snowden is currently eligible, if he wants, to run for a senate seat in Pennsylvania, so he could conceivably be run against Bob Casey, Jr. (Democrat) or Pat Toomey (Republican).
Being a senator would certainly render him as "above the law" as other senators are/have been.