Hi Jeremy,
Unfortunately, It is not possible to create the “delayed” rules - you can only set rules on messages while received.
However, for your need, the auto-archive feature might be useful. In Menu > Tools > Settings > Auto-archive you can set eM Client to move messages “older than x days” to archive folder. These messages will be removed from the server and stored locally. If you need, you can always delete them manually.
Russel