It would not start it. The compressor would try to start but would not run on it. I use the inverter at times with my small compressor hooked to my Dodge pickup. It has two batteries.
The initial amperage requirement for an air compressor would most likely surprise you. I have a 240v compressor that requires a 15 amp circuit, according to the motor label. I have a generator with a 35 amp surge capacity and it will not run the compressor if there is any pressure in the tank. The amperage needed to start your compressor may be three times or more than the running amperage. You need to either run the smaller compressor, or get a larger inverter if you need that particular compressor.
Someone above posted the amperage required to run a device, I'm sorry I don't remember who. No inverter is 100% efficient. Take the wattage requirement for any given device and divide that by 10, that number will give you an approximate amperage draw on your battery/batteries per hour. If you have a 100Ah battery and your load is 10 amps, you would think you could get close to 10 hours running time........no. Batteries are not 100% efficient either, and the higher the load, the lower the battery efficiency. That 100Ah battery in good condition might run that 10 amp load 8 hours, if you're lucky. If that load were to be increased to 25 amps, you might get 3 hours run time. If that load were to be increased to 100 amps, which is only 1000 watts, I doubt you would get much more than 30 minutes.
Being able to run 120v equipment remotely with an inverter, rather than a noisy generator, is an expensive proposition. You need a tremendous battery bank and the ability to recharge it in a fairly short period of time, if you use it most every day. You could try to include that bank in the charging circuit of your tow vehicle, but I doubt any single alternator setup would be able to do much in the time it takes to drive from one job site to the next.
