Watts is Watts regardless of the power source. Power in watts is equal to voltage times current or P= I times E. This is actually Volt Amps or VA which dosn't take into account power factor for inductive cuircuits but is close enough for estimations. 1000W divided by 12VDC = 83 amps of current draw from the battery. A 12V 40AH battery will be dead in less than 1/2 hour at this rate, especially after you factor in the inverter efficiency(or lack of) and the losses of drawing the current from the battery at this high rate(makes a lot of heat). It is also hard on the battery and shortens it's life to draw at this rate. That same 1000 watts drawn from the wall outlet in your home would pull 8.3A. If you are running inductive loads such as power tools, they draw a good portion of their energy from the peak of the sine wave. A inexpensive square wave or modified sinewave inverter will lack a bit of power for motors and therfore will require more energy from the source to run them and they will lack their peak rated power and will stall easier.
For short term use, you can get away with this but I wouldn't do a lot of work like this. Most tractors, having partly been designed by accountants are not known for their alternator output
Heavy inverter use on their stock electrical system will shorten it's life also.
An alternator driven off the PTO to power a bank of batteries could be made into a more robust system. You would however need to gear up the alternator to an acceptable RPM to get a meaningfull output from the 540 PTO RPM.
If you are going to go to the trouble of building the inverter setup, I would reccomend the best of both worlds. Since you need to build up the drive for an alternator at an increased speed anyway, why not put together a small PTO AC generator. Use this with an off the shelf battery charger(AC to DC) and charge a small bank of four 12V batteries(48V total, lower draw per battery, more efficient and longer battery life). This in turn could be used to power an inverter. That way, you have the intermittent use available from the inverter without the tractor running all the time. You have a larger generator for if you need to power a larger load such as a small welder or air compressor.
This whole setup might also come in handy during a power outtage. The generator could power basic home needs such as well pump, refer and freezer and charge up the batteries during the day/evening. The batteries and inverter could provide small ammounts of on-demand power(lights, radio/TV) during the night and in the morning without the need to go out and crank up the tractor.