This is absolutely doable, and is really the logic behind most current physical election security procedures. Procedures are designed less to prevent tampering than to make tampering obvious. Re-voting can theoretically be done, because (public, real-time) records are kept of who voted at a particular polling place, not counting provisional ballots - look outside for a "street index" at your polling place.

(Source: am volunteering for the second time working the physical polls.)