that is something I've wondered for quite a while, and from a quick test that I did, I don't think so - I entered an in invoice logged in as user1. then deleted it logged in as User2. then updated the batch while logged in as user3. when I look in AR invoice history Inquiry Created by is blank ""last Updated By"" shows User3 - the user that ran and updated the daily Sales reports/updates.:(
a similar test with Sales orders provided better results - if you save deleted sales orders in history the ""Last Updated by"" DOES show the user that deleted the Sales Order.