Question about Logitech G G403 Prodigy

Hi,
If by bluetooth you mean wireless 2,4Ghz, i think you can.
In one of the latest LGS (Logitech gaming software for mac) Version 8.87.92. They added those mouse :
Support added for:
G403 Prodigy Gaming Mouse
G403 Prodigy Wireless Gaming Mouse

So in my opinion, yes (Ja).