In theory this will work. 50V should be doable, but once you start getting into the 400V range you have to carefully consider the voltage ratings of your components. For example, your switch transistor has to withstand 400V, and definitely a little bit more for headroom. Same with your diode, inductor coils, etc. Theory goes a little bit out the window as the voltages climb (or, more accurately, you have to be very aware of component ratings and parasitic properties, like the capacitance of your inductor).
Also research the "flyback converter" topology, as that might be a bit safer for your Arduino and you will get a natural voltage boost from the transformer.
: compatible with Arduino UNO, 24V operation, all I/O's fused and protected