Is it viable to daisy chain power across motor drivers?
That doesn't quite look like daisy-chaining. In daisy-chaining, if one element (in your case, the driver boards) were to fail, the whole chain would stop working. In your fritzing schematic, you are using the connectors of one of the boards to supply power to all boards, making it a parallel connection. I'm guessing this is because the battery does not have a distribution rail as such. This arrangement would work but to make it neater you could use a distribution rail connected to the battery and then use that to power everything else.
Second, the Arduino VIN can accept up to 9V. I've seen it work with as high as 12V too. Your battery voltage of 7.2V should be acceptable. That being said, I'm not aware of how the Vm is being derived from the main power source. If it is just being passed through the driver boards then this would work. However, if it is being 'processed' and then made available on Vm then any failure in the driver board would cut off power to the Arduino board.