What you want is a variant of the Sequential Convoy.
Start here: http://biztalkvillage.blogspot.com/2012/12/sequential-convoy-using-listen-shape-in.html
Your Reminder Orchestration would subscribe to messages with data you want to e-mail to the users, either the original PDF emessages them selves or a custom message generated by the existing process.
In your case, the Listen Shape's Delay Shape would be initialized to the time of day you want to sent the e-mail. 4pm, 5pm, whenever.
As additional messages are received, you can build a list or just ignore them. At the end of the Orch, format and send the Message (by smtp).
Either way, the "Files Received" message will only be sent if >0 PDF's arrive.