It would be easy to go with a four . . . i fergit what they are called, but replace the 3 coil part with a four coil, it will make it so that you can have it running with only two split ring commutators. As it is now, you would need three. The beuty of even number coil electric motors is that you can run two coils off of one split ringer. Using the three coil design, you each coil will need its polarity reversed at different times. This means that you need a split ringer for each coil.
So, in conclusion, it will work, but it is inefficient and a wast as it is. Add another coil, get more power, a more continuos torque output, and make it easier to build and run.
Trust me on this.
edit: on seeing your wiring diagram, if you plug it all up correctly, yes, it will spin, but it will not ever be able to output as much torque using that diagram as it would be able to otherwise, here is why(yah!):
you know that force, mag feild, current will always be perpendicular, correct, so you get the most power of of the motor when the pole of the armature is in the plane of the magnetic feild due to the horshoe magnet (the current is flowing perpinduclar to the pole . . its going around it in a coil). But, using your commutator, none of your poles will have current in them when they could provide the most torque. this is bad and needs fixing.