Hello,
Although I have never tried it, there's no reason why it shouldn't be possible. It would probably take significant changes to the gamepad and robot code though.
Although bluetooth with have some packet errors here and there, it actually works very well with the hexapod. Our protocol has error detection and it simply ignores bad packets and assumes the prior command should just continue. Since a new packet arrives every 100 milliseconds this works very well. If no valid packets are received for a full second the robot stops all motors until a valid packet arrives, as a failsafe. In practice this works in every environment I've ever run the robots in, and that includes huge maker faires where hundreds of people with bluetooth devices were in range of the robots. I've also run up to 15 hexapods in the same room with no control issues due to bluetooth's frequency hopping scheme.