I tested a few scenarios... With my phone awake, I sent an Exchange test message. Both Outlook and phone notified immediately. Then, I put the phone in lock and sent another message. The watch notified about 60 seconds late. Last, I put the phone in lock mode, sent a message, and then I unlocked the phone and read the message on the phone. No notification on the watch. To my knowledge, I have not missed any email, message, or other notifications on the watch. They may not have been timely, but they always arrive.