It depends on a couple of factors. A student should understand what educational records consist of. Often there's an academic transcript at a college or university, which reflects, as the name implies, the academic circumstances. There's also a disciplinary record, which is separate from the academic transcript. These records are protected by FERPA, the federal law that protects educational records. But schools would give a false sense of reality that no one can see them unless they're authorized, which is true. But to apply to graduate school or some employment, a student does have to authorize records to be disclosed.
With that being said, the sanction itself, if a student is separated from the university, say a suspension, although it may not be specifically referenced on an academic transcript, there's going to be a gap which would potentially have to be explained. If a student could say, "Got expelled." It's a completely different consideration yet. Probation, lesser sanctions generally wouldn't be reflected on an academic transcript, but it does depend on the particular school and particular circumstances at hand.