Non-priviledge way to restrict UPD/DEL to user knowing certificate pass
Is there a way to restrict a column to only accept updates or deletes if a specific key is open?


No, a sysadmin or someone with sufficient permissions could change the data regardless of encryption.

Should the question or investigation change to be something where it doesn't matter if the data could change but that it was encrypted or otherwise unavailable to a sysadmin or someone with sufficient permissions, then yes that is possible but would require the keys to be stored outside the database system or for secret passwords to be known (less secure).