Officers that are impeached by the House and convicted by the Senate are disqualified from holding an office of honor, trust or profit under the United States, which means that they can’t serve as President, VP, Cabinet secretary, ambassador, federal judge, or certain other Article II or Article III officers, but it is no impediment to serving as a Representative or Senator. Similarly, an ambassador is subject to impeachment, but a member of Congress isn’t (members of Congress are subject only to expulsion, which would not disqualify them from future election).
I read somewhere that the Senate could have disqualified Alcee from being elected to Congress but didn’t.
Thanks, faulty source!