Yes but its not just about the beam. Signal timing can be used for more precise location. Even with one sat receiving the signal. Because they move so fast, much faster than the user could possibly move. So it basically could triangulate with itself as the other receivers. And there's also Doppler like the other poster mentioned.

I don't know if they actually do this, I guess not. And it would not be simple to do. But I'm sure it can be done. There's enough information available.