If a person was in the middle of space would their cell phone work? How...

It depends on the strength of the signal the phone puts out and the distance the person is from any sort of receiver. The strength of an electromagnetic signal decreases with the square of the distance between two points, so the farther the person is from a receiver, the less likely he will be able to contact anyone. Bluetooth is much less powerful than a phone and has poor signal strength, so I doubt that any receiver can pick it up even from a few meters away.

Distances aside, he will be able to make a call because electromagnetism can travel through empty space.