Not unless you only remove alerts that are read, and then remove unread alerts for a longer period of time, meaning there would be 2 different settings for each.
Ummmmm, why should they expire automatically? Save the query for something else and set everything to manual please. There are times when it's either not convenient to log on, or I just don't plain have access. As I can be on the road for 2-3 weeks at a time, this just doesn't make sense to me.