Do you have a multimeter that can measure current? If so, hook it up to your 'idle' circuit and measure how much current the stepper is drawing while idle. This will tell you quite clearly whether leaving the battery connected will drain it much faster. In fact, you can easily calculate approximately how long it would take to drain the battery, since you know it's a 6AH battery.
If you measure the circuit drawing 100mA while idle, then it will drain the battery in 6AH/.1A = 60 hours.
If you measure it drawing 1.3A, then it will drain the battery in 6AH/1.3A = 4.6 hours.
If it's only drawing 20mA, then it will drain the battery in 300 hours.
With your control circuit 'off' though, the stepper really shouldn't be drawing any current at all.