Absolutely. David Petraeus had his entire career ruined over an incident of far lesser severity. Besides:
Federal Records Act 1950 as Amended
18 U.S. Code 2071
(a) Whoever willfully and unlawfully conceals, removes, mutilates, obliterates, or destroys, or attempts to do so, or, with intent to do so takes and carries away any record, proceeding, map, book, paper, document, or other thing, filed or deposited with any clerk or officer of any court of the United States, or in any public office, or with any judicial or public officer of the United States, shall be fined under this title or imprisoned not more than three years, or both.
(b) Whoever, having the custody of any such record, proceeding, map, book, document, paper, or other thing, willfully and unlawfully conceals, removes, mutilates, obliterates, falsifies, or destroys the same, shall be fined under this title or imprisoned not more than three years, or both; and shall forfeit his office and be disqualified from holding any office under the United States. As used in this subsection, the term “office” does not include the office held by any person as a retired officer of the Armed Forces of the United States.
Especially note: "be disqualified from holding any office under the United States."