Yes, you can. Look here. You can set schedule in agent's properties:
You can select which documents will be selected. In example will be all database's documents selected. If you select "None" it's up to you to select your documents in agents's code in a e.g. NotesDocumentCollection.
For your case the easiest will be to select all documents and add an if statement to test if document is not yet in target database:
Set docSource = col.Getfirstdocument()
While Not docSource Is Nothing
If docTarget.GetDocumentByUNID(docSource.UniversalID) Is Nothing then
Set docTarget = dbTarget.Createdocument()
Call docSource.Copyallitems(docTarget, True)
docTarget.UniversalID = docSource.UniversalID
Call docTarget.save(True, False)
Set docSource = col.Getnextdocument(docSource)
End If
Wend