Yes, yes – that’s right! Mobile LinkedIn doesn’t have it, iPhone’s app doesn’t have it. But DroidIn does!
You asked and we listened (sorry it took some time) . Starting with 1.5.0 release both DroidIns have Inbox feature. The inbox has some limitations: Lite users will be able to check the list and open messages. Full version users will be able to reply but only to the original sender. They will also have message sent to their own mailbox.
The search now is available to all users, the UI was updated
Please report any bugs or just give us a feedback – it’s always nice to hear from you

Is it possible for DroidIn to create Synergy-like implementation into the ContactList for all LinkedIn contacts, including phones, emails, photos, additional contact data. Maybe a 24hr-chronjob in the background – Alert that starts a service – that syncs LinkedIn with ContactList?
I don't really understand the question. Where the ContactList is coming from? Can you elaborate?