Examples of Congress being charged while in office:
https://www.nytimes.com/2018/08/08/nyregion/chris-collins-insider-trading.html
Politicians convicted while in Federal office:
https://en.wikipedia.org/wiki/List_of_American_federal_politicians_convicted_of_crimes
Oops, omitted this qualification which was contained in the citation at the link:
“shall in all Cases, except Treason, Felony and Breach of the Peace, be privileged from Arrest during their Attendance at the Session”