I'm pretty sure there are no provisions for this feature running down in the radio micro-code (which is turned off during sleep).
What about a scheme where the transmitter sends a burst of 60 "magic" BLE packets 25ms apart.
The battery powered receiver wakes up once every second and listens for a magic packet for 50ms
then goes back to sleep if it does not see a magic packet.
How quickly can the a WICED device wakeup from sleep, receive a packet and go back to sleep ?
Yes, you should be able to create this feature at the application level. Sorry if I mis-interpreted your original request which was to have the Radio perform the sniff/wakeup event while the on-board ARM MCU is asleep -- which it (the radio) cannot do at the hardware level.
There are different modes of sleep available (and the application can participate in the decision of "if" it should go to sleep). Refer to this really well done article: Sleep Deep_Sleep Explanation and Techniques
It also talks about the wakeup latencies affiliated with the various sleep modes.