Yes!  There are a couple of ways we will be getting the member's attention:
  1. At the top of the member's main page we'll present a new message banner indicating they have messages waiting to be read.  The member can click View or Dismiss:
    Picture of the banner message  
  2. Also, when the member clicks the Profile button in the upper-right corner of the screen, a circled red number will indicate how many messages are waiting to be read in the Secure Message Center:
    Picture of the profile menu