I've been mulling this idea over, and something occured to me. At first I thought it was an obvious good idea, it seemed like a no-brainer. But then I realized something:
If the Address Book was really easy to use (sort and find people) then what would stop people from just adding every single name they come across to their address book? If this idea was implemented, I would see no real downside to just spamming your address book full of every JSP user you see. This way, if you ever decided you wanted to look someone up you'd have a quick way to do it and all the names you never use wouldn't be in your way.
If people started doing this, would those huge address books be taking up space on the server that hosts JSP? Probably so. So I think if this suggestion was done, there would need to be a reasonable cap on the size of the Address Book (maybe like 100 names) otherwise I just see everyone adding everyone.