Can I bench test a N-channel MOSFET with battery, oscilloscope, and arduino alone (no applied load)?
It will switch, but you won't be able to see it, since the oscilloscope can only measure voltage. You need to give it some voltage to measure, and the easiest way to do this is to connect a power supply to the drain of the transistor through a resistor. For example, if you have a 5V power supply, a 1000&Omega; resistor will pass 5mA, and you will easily be able to see the difference between MOSFET on (near 0V) and MOSFET off (5V).