The short answer is YES.
Where the magnets face each other with the rotor between them, the flux is perpendicular to the surface of the rotor. Lets call this surface the 'front' surface. At the 'back' surface, there needs to be a magnetically soft iron ring to conduct the flux between adjacent magnets.
These motors/generators generally have a winding which loops around each magnet, which is connected to the outside world and this winding is for magnetising the magnets.
I have a couple of these machines, often called 'pancake' motors, and they seem to suffer from demagnetising problems. I cant say why, but thats how I came by these machines.