You could do so, but when listening to the stereo without engine runnig you will risk to empty your starter battery. Therefor i would install a relay, that disconnects the starter battery when listening while engine is off.
the isolator protects your car's ability to start as well as it protects the batteries themselves. If you run a normal starter battery below about 10 volts, you'll damage the cells and the battery will have to be replaced, or it will prevent your car from even being able to run properly. Isolating a deep cycle battery and using that for the audio system, you can run it all the way to zero volts and it won't damage the battery itself. that's why we use deepcycles, and we don't just parallel them with the starter battery.
@ glasswolf since im not so familiar with English what the difference between isolator and a relay? As i understood the device should seperate the starter batterie from the audiosystem batterie. But with the engine running it should be connected to charge. Is that correct? Sorry about answering without beeing asked? Dirk
the term "relay" generally refers to a Bosche stype relay, which are used throughout car audio systems for many reasons. a battery isolator is what you described, allowing current to flow to all batteries for charging purposes and to power the systems while the engine is running, but "isolates" the starter battery from the other batteries when the car is off and current is being drawn from the isolated batteries, preventing the starter battery from being drained by the stereo. an isolator is generally a network of relays and diode arrays with a hatsink large enough to handle the high current flow from the systems. You can get them from any RV supply shop.