Is there a smart-wake yet?

[treebeard]

The phone will wake on incoming SMS/MMS.  I think the closest you can get right now timer-wise is the "community" modem firmware has some capability to wake the phone at specified times.  Waking on incoming email seems like a tough ask.  It seems like your email provider would need a way to ask your cell provider to wake you.  Maybe your email could be rigged to send you an SMS under certain conditions?

Edit 1: on second thought, maybe by "chats" you meant IRC/matrix/xmpp etc. Then I think it would be similar to the incoming email problem.