The extra load of the choke would increase current in the coil circuit. That increased current would and the addition of the choke, would change the voltage drop across the ballast resistor. Seeing as the circuit is not just the run ballast resistor and the coil, but has the choke in parallel with the coil, the voltage available at the coil would change. How much? Don't know. Probably not a lot. You are increasing the load on the ballast resistor though.