"Satellites and space ships orbit at approximately 150 miles above the earth's surface. Given that a standard phone only works within a 10 miles radius of the tower, the satellite or spaceship would need its own tower. This tower would also need to be located on the outside of the space ship otherwise the metallic structure would block the signal. You would also need a dish antenna back on earth tracking the satellite to receive the signal."
-Techsling
This is a piece of text from an article so I advise that you do not copy and paste it or you might get in trouble.
So maybe it would but it would be extremely hard to do it.