As per my experience you get a little bit of cross talk due to the proximity of the two inlays already but if you were to try to add in something like this to the ring itself things get a little more complicated .
You should have to have a system to switch it on and off if it's in the ring.
Also you can try to switch the IC out for the LED, because running the LED as well as the wafer doesn't leave much power.

pcb prototypes