Using EMG pickups as a reference. On average, per pickup takes about 3000hrs to drain a 9V flat. Lets say u use 2 pickups, so double the current, u should have 1500hrs.
Even if it's left plugged in for 24/7 that would still give u 2 full months of battery life. I doubt an el cheapo battery would have 1/8 the battery life of a Duracell either. :mrgreen:
Anyway, once the battery starts to die, the voltage drops, u lose headroom. U can tell when the sound starts to distort.
Also, the effects that a guitarist uses has it's own power supply, it doesn't drain from that battery.