Nice idea, but I think you'd need so many external components that the Arduino would be redundant! The ATMega itself is fast enough, but doesn't have nearly the i/o bandwidth you need - getting data in from the ADC, out into external RAM (the 1k that the ATMega has won't get you very far), back in again from RAM, back out again to the DAC just isn't going to happen at any useful sample rate.
Something like an ARM7 / ARM9 board might be better suited to this (iirc they clock at about 50MHz), or one of the dedicated DSP evaluation boards.