Hmmm...well I'm not an expert, but it depends. Are you looking to cleanse your body as well as lose weight? If you are I would say no. If you can help it, you don't want to be drinking any kind of sodas.
However, Diet coke really doesn't have anything in it so if you are doing a fast for weightloss, it might not have much of an impact. Of course it may effect your results. Take this with a grain of salt though. I can't be sure of this.