Using a motor startup current calculator, with perfect power factor and efficiency (i.e., both values = 1 instead of more realistic values like .84 and .9), and with the advertised 1200 Watts of running (not startup) power at 120V, the startup current would be 23.09 Amps. With pf=.84 and efficiency=.9 instead of them both being 1, the calculator yields 30.55 Amps on startup. Assuming you start the bandsaw unloaded (i.e., not trying to cut anything while starting up the motor), this high inrush current should last less than a second, maybe three seconds max, since it will reach full speed (Locked Rotor Torque) in that time period. The current will gradually decrease to standard operating current. If the inrush current lasts only about half a second, I wouldn't be too worried, but I'd be a tiny bit more worried that small wires' (if they exist here) insulation would get fried if it lasted longer than 3 seconds. As for whether there's even enough current to start the device, the advertised surge current provided by the inverter is 3000W. Using P=IV, that gives an instantaneous (i.e., looking at a singular point in time) current of 3000W/120V = 25A. Though 23.09 Amps (ideal) < 25 Amps, 30.55 Amps (practical) is not less than 25 Amps, so there's likely not quite enough startup current to get your bandsaw running, unless your vehicle supplies extra power (like by spinning the alternator faster by "giving your vehicle gas") and the inverter somehow deals with it in a way that increases your surge current output.
P = IV -> I = P/V -> Current = Watts/Volts -> 1200Wbandsaw/120V = 10A (of load, not supply).
Environmental factors:
- Dust buildup reducing heat transference away from the bandsaw motor -> the motor wiring heats up more, meaning it will draw somewhat less than 10 Amps (by how much? I can't say aside from "probably not a huge difference") due to the higher wire resistance (V=IR: if R increases while V stays constant, I must decrease)
- However, once the "blade" dulls, you'll probably push the blade holder so that it has more pressure to cut with, which places more physical resistance on the motor, which brings it more out of phase, which draws more current (same principle as startup current where the physical rotation speed doesn't keep up with the electrical "rotation speed" (phase)); this is a far more significant factor to current draw than the motor heating up a bit.
- As the other answers/comments mention, if you baby how much material you feed into it (decrease the load), you should be fine (barely).
- There's often corrosion on people's vehicular battery terminals and lots of vehicle parts can somewhat deal with having undervoltage (meaning nobody fixes the problem because it doesn't look like there's a problem). Make sure there's a strong electrical connection and no corrosion first, to make sure that the inverter is receiving enough current to produce 120V. Supplying too little voltage for the same load means excess current is drawn (P=IV: if P remains constant and V decreases, I must increase), which could fry your vehicle battery or inverter or bandsaw.
tl;dr Your bandsaw will probably work (once you get it to start moving), but be careful with how far you push your bandsaw.