Yes it can be done but you need to upgrade your battery setup to run it...
I have a always ON 120VAC 600WATT AIMS PURE SINE WAVE setup on my OFF-ROAD POPUP trailer. This runs off my 255AHs 12VDC BATTERY BANK. This will draw around 50AMPS DC Current from my battery bank if fully loaded down. MY high drain is usually between 4PM and 11PM each evening and usually only 1-2AMPS DC drin during the other time periods. The most I see on my Battery Monitor system is around 22-24AMPS DC current between the evening hours running all the things we want to run off our batteries..
I have two multi-tap 120VAC OUTLET drop cords plugged into it with one going to the Home Entertainment items and the second ne going back to a cabinet table top to run my USB chargers, Computer chargers, and a couple of other emergency type items I always want to be powered up...
My floor plan looks something like this...
Google Image
I currently have three each 85AH 12V Interstate Batteries in my battery bank giving me my 255AHs of capacity. This has all failed last season after being install in early 2009. I am currently in the process of install a new Battery Bank for two groups of two GC2 6VDC batteries in series which will give me a 440AH battery bank capacity.
Roy's Image
This is probably alot bigger than you want to do but having a always ON 120VAC and 12VDC circuits fits my needs just great...
When camping off-grid I have everything planned out to run all the things we want to run in a one/night run off the batteries and then use my 2KW Honda Generator each morning starting at 8AM to re-charge my battery bank back up to its 90% charge state state which takes around three hours of generator run time. Then I am good to do this all over again for the next day/night run off my batteries...
Been doing this working routine since early 2009...
Roy Ken