No, when the arduino is put to sleep, the processing of code is halted. The arduino either needs to be woken up by a watchdog (a timeout) or an interrupt (hardware event) to resume processing code. I'm pretty sure that somehow the bluetooth tranciever should be able to generate an interrupt, so that the arduino only wakes up to process bluetooth request and when done can be put to sleep again. But this would require the bluetooth tranciever not to be put to sleep / powered down.
kotran:
but is it possible for arduino pro mini to receive data when arduino pro mini is in sleep mode?
No its not.
What you could arrange is to put the Pro Mini to sleep and leave the Bluetooth receiver powered so that when it receives some data it wakes up the Pro Mini.
And no, the Bluetooth receiver cannot receive data when its powered down .......