The suspension will be a part of a student's disciplinary record, whether it will be part of a student's permanent disciplinary record, is a different question. When a sanction such as a suspension is imposed, it will go on a student's disciplinary record more or less regardless of the college or university involved.
Regarding whether it will be there permanently, that will depend on the school's particular policies. Some schools have specific policies that a suspension will remain for ever. Other schools have policies that a suspension will remain for a period of time, say seven years. Other schools will have policies that upon completion of a sanction or upon graduation, a student can petition to have a disciplinary record vacate it. Other schools are vague about that. All those steps can potentially be taken to try to negotiate such a resolution.
Suspension, although it may not be on a student's academic transcript, there will be a gap or a period of time where the student was not there. So in a sense it is also reflected on an academic transcript. Suspensions can be rectified. Steps should be taken as early as possible in the process to avoid a suspension. An experienced attorney advisor can help both navigate the process and if a student is suspended, it can help with the appeal process.