the order you turn on the RAMPS and the Arduino shouldn't make any difference. Some people have noticed that the Arduino may reset when you power up the RAMPS board.
As for disconnecting the drivers while running, yes it's a possibility. Some people have been lucky, others haven't. I suspect that if you click the "Motors off" button in Pronterface (or send the equivalent G-code), wait a few seconds then disconnect the motors you will be fine, but considering the cost of stepper drivers, it makes sense simply to power it down properly.
FWIW: If anyone is building a machine, I recommend you test the steppers before connecting them to any board. I helped someone who fried a stepper driver - turns out that one of their steppers (was one of the Z steppers) was a dead short on one coil, and he ended up with a small hole in his stepper driver and a bit of smoke. Had he tested the coils on the stepper first with a multimeter he'd have found that one of the coils was bad and saved himself the price of a new stepper driver + shipping (and the wait for the thing to arrive).
As for disconnecting the drivers while running, yes it's a possibility. Some people have been lucky, others haven't. I suspect that if you click the "Motors off" button in Pronterface (or send the equivalent G-code), wait a few seconds then disconnect the motors you will be fine, but considering the cost of stepper drivers, it makes sense simply to power it down properly.
FWIW: If anyone is building a machine, I recommend you test the steppers before connecting them to any board. I helped someone who fried a stepper driver - turns out that one of their steppers (was one of the Z steppers) was a dead short on one coil, and he ended up with a small hole in his stepper driver and a bit of smoke. Had he tested the coils on the stepper first with a multimeter he'd have found that one of the coils was bad and saved himself the price of a new stepper driver + shipping (and the wait for the thing to arrive).