Just by running two batteries you will get cleaner sound, if voltage drop is the problem for the amp. Moreover, if you run two separate battery then you can run higher voltage amps as well since they are not tied to the 7.2v or 7.4v battery with the MFU.
The input power can be completely separate for the amp. You can also do this for the smoker. We use TARR smoker and I have run it separately with a 3S lipo (11.1v).