Not if he's actually removed by the Senate. He's unable to hold office again of any kind in the federal government if that happens.
Article One, Section Three, final paragraph:
Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law.
Edit: But, let's face it, he's never being convicted in the Senate based on the evidence provided by Schiff.