Wireless glove mouse - UART, Bluetooth confusion?

Hey everyone! So my project aims to develop a glove-mounted design which will wirelessly communicate with a computer, telling it where to move the mouse, as well as sending things like mouse clicks.

I've gotten it to work tethered using the Mouse library, but now I'm at a roadblock- UART.

I'm looking at this one chip, Adafruit Bluefruit LE UART Friend, which can act as a transparent data pipe. I'm thinking I'll use two: one for the glove Arduino which will send packets, with another one for the base station connected to the computer, which will receive packets to interpret.

When it comes to UART, if the transmitter side doesn't mess with TX and goes about its business without using the Bluetooth chip, will the receiver chip just receive nothing? My biggest worry is that if the transmitter ignores the chip, the receiver will just receive garbage.

Adding to that, is it possible for the transmitter to do its own business without the Bluetooth chip for extended periods of time? I'm asking because this design uses I2C to communicate with an IMU, and I'm worried that servicing a Bluetooth transmission in the middle of an I2C transaction would ruin the IMU communication.

Hopefully this question helps out others who are confused about the magic going on with wireless communication!