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An 1800W inverter feeding an 1800W appliance *might* work. When they measure wattage, there are peak (AKA surge) and continuous values. Inverter manufactures tend to advertise the peak number, since it's bigger. Appliance manufacturers tend to advertise the continuous number, since it's smaller.
When an electric motor starts up, it uses a surge of electricity far greater than what it requires when running. That's why you might see the lights dim momentarily when your A/C compressor kicks in. If the appliance surge exceeds the surge capacity of your inverter, then you need a bigger inverter. Since you already own these devices, it can't hurt to try it and see how they interoperate. Keep in mind that the inverter requires ample DC voltage input in order to produce its max rated output.
The device documentation should tell you the surge requirement for your appliance and the surge capacity of your inverter. This documentation will also tell you where you need to put fuses in your circuitry. Be very careful to comply with this guidance. If you don't know enough to install proper fuses, find someone who does. Any professional mechanic will know. Fuses and/or circuit breakers are essential safety equipment. They prevent electric fires if something goes wrong. Do not omit them.
If you run the A/C with the engine off, you can drain the batteries to the point where the truck won't start. This is why many folks have a separate "house" battery, plus a battery isolator to keep the starter batteries just for starting.
Watts=Volts X amps. 1800W @ 120 VAC = 15 amps. A normal household outlet and the circuit breaker behind it are rated at 15 amps. This means that A/C unit is designed to max out a typical household circuit. You have to feed at least that much power into your inverter. Inverters are never 100% efficient. You always lose some power in the conversion process. Ignoring that for the moment, 1800W @ 12V = 150 amps. That's a *lot* of amps. What is the capacity of your alternators? If they can't produce over 150 amps, the inverter will draw down your batteries even with the engine running.
Your inverter documentation should tell you how many amps it draws at max power. The number will be more than 150. How much more depends on the efficiency of the inverter. More efficient inverters are more expensive. You may find you need to upgrade to bigger alternators to handle this load.
You can see why most RV folks use a generator to power their A/C units. They take a lot of power, and it's expensive to upgrade a 12VDC system to support an inverter that provides that much power. A little Honda generator is usually a less expensive option. It's also much quieter and much more fuel efficient than a 6.2L V8.
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