Projector audio output

[Cadcro1]

If I purchase a pair of Bluetooth 2 in 1 (transmitter/receivers) and connect one to a projector 3.5mm audio out jack and the other in receive mode to a speaker 3.5mm input jack can I paint the two to receive the projector audio out. The home cinema setup I plan would require this setup.
Cadcro1

 

[Cadcro1]

MERGED QUESTION
Question from Cadcro1 : "Projector audio output"

Sorry about the typo previously. I wish to pair the two, not PAINT them.
Cadcro1

 

[americanaudiophile]

It should work but
1. Your projector has to pass audio from the HDMI input which is digital audio. Some don't convert digital audio to analog. You can check this by connecting a speaker directly to the projector audio output.
2. You will not get digital surround sound as the output of the projector will be 2 channel analog (BT only supports stereo as well). You can use any surround modes on your HTS, such as Dolby Prologic2, that are meant to derive surround sound from 2 channels but it won't be as good.