Q. Can I time an announcement to have an open and close date?

Just an Open Date.

An announcement can be given an open date in the future by using the "Delay Posting" option. NOTE: if you are including a time, you must click "Done" in the calendar box or the time will not save and default to 12:00AM on the given date.

There is no option to close an announcement by a specific date. Once an announcement is published, the only way to remove it is to permanently delete it from the course.