?? Not sure the connections will fit.
Since the ADC is similar to DVI-I in that it can carry both analog and digital signals it should work.
The issue is going to be in the physical connections. The mini displayport to DVI adapter is DVI-D (digital) only. I have not seen, nor ever used ADC, but my best guess would be that the DVI to ADC adapter has a DVI-I connector which has 4 pins surrounding the long pin. Which means, the adapter you have, will have too many pins to fit into the DVI-D on the mdp to DVI as it does not have the openings for those 4 pins.
Take a physical look at your existing DVI adapter to verify. I have seen a DVI-D to DVI-I adapter, just don't have the time to go hunting for it at the moment. And it is only my best guess that it would work. You would end up with 3 adapters to get it working - mdp to DVI, DVI-D to DVI-I and the DVI to ADC.
(I have also moved this to it's own thread. It is not the same as the issue related to VGA connections.)