The battery/batteries have to supply same amount of voltage that is present on the power supply rails. A 100 watt/ch receiver could easily need as much as 54volts positive and 54volts negative. Thats a lot of car batteries in series.
In addition to the main supply rails there will be many other lower voltages present taken from multiple taps off of the transformers secondary winding. You will have to duplicate these DC voltages as well.
It might be possible to isolate just the main power supply rails to the output stage and graft in the battery voltage just ahead of the power supply caps for this voltage value. I would bet on it being a major PITA to do, however you could get lucky.
This winds up being a vary involved project whose sonic benefits are questionable when applied to the circuitry found in a typical receiver.
Battery power supplies are usually applied to simpler pieces of gear like preamps and power amps. These applications usually require only one voltage to be applied at the location formerly occupied by the rectifier and immediately ahead of the main storage capacitors.
Speaking for myself, I would give this idea a pass.
Scotty