The append period is part of the equation. Your append period specifies whether a job is allowed to append to a tape or not. Similarly, the overwrite protection period controls whether a job is allowed to overwrite a tape. The job settings then dictate what the job will actually do.
In the case where the append period is none (append not allowed) and the overwrite protection is none (protection expired), a job can overwrite the tape. A job cannot append to the tape. If the job is configured as the default (append first, then overwrite), the job will first "try" to append to the tape (which won't be allowed), and then it will "try" to overwrite the tape (which will be allowed).