First, the speech and debate clause is not an absolute protection for Howdy Gowdy but only protects official acts
http://legal-dictionary.thefreedictionary.com/Speech+or+Debate+Clause
The U.S. Supreme Court has gradually defined and redefined the Speech or Debate Clause in several cases over the years. The first case concerning the Speech and Debate Clause was Kilbourn v. Thompson, 103 U.S. (13 Otto) 168, 26 L. Ed. 377 (1880). The Court has interpreted the Speech or Debate Clause to mean that members of Congress and their aides are immune from prosecution for their "legislative acts." This does not mean that members of Congress and their aides may not be prosecuted. Rather, evidence of legislative acts may not be used in a prosecution against a member of Congress or a congressional aide.
The main controversy surrounding the Speech or Debate Clause concerns the scope of the phrase "legislative acts." The phrase obviously encompasses speeches and debates on the floor of the Senate or the House of Representatives. According to the Supreme Court, voting, preparing committee reports, and conducting committee hearings also are legislative acts, but republishing legislative materials for distribution to constituents and accepting a bribe to influence a vote are not.
Howdy Gowdy's actions were not within his official legislative duties but were for the purpose of damage control to attempt to preserve what little reputation that Howdy Gowdy had remaining after this partisan exercise. As such, there is a good claim that the speech and debate clause does not protect Howdy Gowdy.
Second, the main causes of action are under two separate statutes that expressly provide for damages due to congressional actions and so are not subject to the speech and debate clause.
Finally, Paragraph 99 of the petition makes clear that the Plaintiff is not seeking damages against Gowdy but an injunction. The speech and debate clause does not apply to an injunction. Here is Paragraph 99 of the petition:
Plaintiff does not seek any damages associated with his common law defamation claim against Chairman Gowdy. Instead, in asserting his common law defamation claim, Plaintiff seeks equitable relief in the form of a declaration that Chairman Gowdy made false and defamatory statements about Plaintiff and a permanent injunction barring Chairman Gowdy from repeating the same false, defamatory, and injurious statements that he has made about Plaintiff beginning on October 10, 2015. Without such an injunction, Chairman Gowdy will likely continue to repeat the same false and defamatory statements about Plaintiff, which will cause Plaintiff to suffer further harm from the repeating and further publication of such injurious statements
Howdy Gowdy will attempt to use the speech and debate clause but I doubt that he will be sucessful