I use stock Rom, non rooted, and default mail app (not gmail or anything).
If I go as far as to read the email on my gear, by default it shows up on the phone as read.
But you can't delete an email from the phone through the gear. At least not from what I've seen.
Sent from my SM-N900W8 using xda app-developers app
My trek through cellphone history:
Nokia 252 - Green
Mitsubishi Trium Astral - White
Samsung Omnia II
HTC Desire Z
Samsung Galaxy Note 1 - 16GB - White
Samsung Galaxy Note 3 - 32GB - Black **Surprisingly, under warranty, they even fixed the physical damage I caused. Go figure...**