Of course. Bluetooth acts here as just an input. A relay is an output. The key strength of Arduinos is taking specific inputs and turning that into specific outputs. But it's not going to be exactly low power that way of course, with the power needed to run that bluetooth transmitter.
Just be aware that "within range" is a very ambiguous actual distance. Can be as little as 1 meter, can be as much as 100 meters.