Depends. Running your receiver hardware continuously to see if someone is requesting information often takes much more power than just briefly and occasionally turning your transmitter on and sending a short burst of data. You could periodically power on and poll the receiver instead, but it's still not necessarily better.
For example, a typical low-power RF transmitter chip like the CC1000 (http://www.ti.com/lit/ds/symlink/cc1000.pdf page 7) consumes 7.4 mA in its lowest-sensitivity receive mode, or down to 5.3 mA in its lowest-power transmit mode. Either one can be reduced by turning the transceiver off and on, but you're still better off just using the transmitter occasionally.
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