I wouldn't run this because it would be 2 pre's. As far as i know you can't bypass the pre in the AD-20. If you really want to run the mini-mp pick yourself up a GP ADC-20.
Denecke sells a 16db attenuator cable that is used to negate the preamp gain in the AD-20 if you choose to run a pre in front of it. I still would not recommend doing this.
I would investigate a modSBM way before considering running an ADC-20. I ran both of these and much preferred the modSBM. True, it costs a little bit more, but is well worth it.
I agree with the other opinions who have stated that the thing to do is sell the AD-20 and pick up a used MiniMe instead if you are thinking of a MiniMP > AD-20 combination. If you are on a tight budget and want a significant upgrade, think about selling the AD-20 and go with transformers and a modSBM-1.