Yes Marc. The way you had laid out is one way that people get away with a full wave rectifier without floating the ground. The downside (on a bike that has a frame ground originally) is that everything on the bike must be floated and rerouted back to the negative of the rectifier or in your case the battery. The power lead must also be "floated" back to the battery.
The frame must ONLY be used by the other side of the rectifier and one side of the coil (the grounded end). This in fact WILL give you full wave rectification. It will not be the cleanest power due to the frame being used as a conductive path but the AC pulse will oscillate back and forth properly.