When I first posted in this thread,idea/experiment had not been done and it was still in everyone head. Now some stuff has been done to enhance our use of the NFC Ring.
Initially, I thought of a modificaton that would enable the nfc sensors even when the screen is off. I don't know how much battery drain that would cause, but maybe a lot because the sensors always need to send pulse ?
Of course, better methods are available : when the Moto X was released, it pleased everyone with it's active notification system. With the good ideas, some users created programs to duplicate Moto X features like "Gravity Screen", "Active Display", "Ac Display" and so on.
The software "Gravity Screen" allow to turn on the screen when it detect that you take your phone out of your pocket. It does this by using the proximity sensors (used to turn off the screen when you are talking to someone to minimize touch event) and this method is very good for the battery. Then, as the screen is on, the nfc should start working and your phone will unlock itself in your hand. Nice! I take my phone and it's already usable.
There is other software than this one to do the job, and it can also be done using tasker, but with tasker the proximity sensors detection is just to slow and you get too much false positive/delay.