I've never had that big of an Power Inverter but even my 600WATT unit really draws the DC power from the battery setup. I'm pulling 22 AMPS every evening from 6PM to 11PM and my 255AHs battery setup will drop to around 50% charge state by 6AM the next morning. This is when I bring them back up to their 90% charge state using my 2KW generator setup for three hours. Been doing this metho for several years now and still have the same batteries that were installed in late 2008...
The 2000Watt Power Inverters will be pulling in excess of 170AMPS from your batteries when loaded down. Gonna need some good batteries for this... You will want to know how long your batteries will hold up with that much WATTAGA being pulled and only drop to their 50% charge state (12.0VDC). You can look up your battery Reserve Capacity specs which is usually listed in minutes and then divide that by 2 which give you the 50% capacity. I suspect my battery bank might last 30 minutes doing this much DC Current load...
I would also insure the Power Inverter is a Pure Sine Wave type then you never have to worry about what is plugged into it. I have found anything with Motors and Electronic Circuits are prone to fail using the Modified Sine wave units... My fan motors hum loud and get real hot and don't spin up to max when using MSW Power Inverters.
Just some of my comments... I have also heard that high end high dollar MSW Power Inverters are better than the cheaper auto parts store version Power Inverters for what ever that is worth... Read up on what others have to say...
Roy Ken