I was playing at connecting wires to 'get the feel of it' when I accidentally connected the servo connector red wire to the arduino 5V pin while the arduino is connected to my comp, (and hence powered). I did not connect a battery to the ESC though. Did I just effectively ran 5 V through my BEC and risk damaging it? What I only managed to find online is I shouldn't have done that when the battery is connected because I will burn out my Arduino. But since I didnt have my battery connected to the ESC, will my BEC get damaged instead? I couldn't check my ESC now because I don't have any suitable batteries with me right now and I have to wait till Monday to get my batteries. Just thought I can find a quicker answer here.
Should be fine. If I remember correctly, the inputs to the ESC (more or less) control power mosfets. Putting input to a mosfet without power does not hurt it.