Batteries can soak up and buffer fluctuations in alternator voltage, not unlike how a large body of water can buffer out fluctuations in the temperature of the air around it. Running an alternator without the battery will at a minimum put more electrical noise into your system than if the battery were connected. In the worst case scenario of a runaway alternator, the battery is the load of last resort to soak up the excess production and hopefully keep your avionics from being destroyed. Worth observing that the classic Cessna split master switch is purposefully designed so that it is impossible to turn on the alternator without the battery master already being on.