David,
What are you looking to achieve? I can see saving the read messages to the AC chart if you are looking to document their read of the message - is that part of your process?
Based on my conversations with practices, they are more interested in those reminders that come back when a message isn't read. That typically requires additional staff work to follow-up and get the patient to read their messages. That then becomes a question of the most efficient workflow for the practice.
