Aaron,
I would say a very large number of inverters don't get used when the engine is running. You'd only have to do that if you were pulling down you battery too fast.
At 200 watts you'll consume about 17 amps on the DC side; your 140 AH battery would be good for about 4 hours at that rate if you wanted to keep your battery above 50% depth of discharge. Take a look on the labels of the things you want to run; they'll normall have the wattage or amperage draw on them. If it's watts divide by 115-volts (usually what they're rated at) to get amps. Multiply amps by 10 to get from the AC side draw to the DC side draw (this also takes into account the loss in the inverter). If your battery is fully charged you'll have about 70 AH to use to stay at the 50% or better mark (you can go lower depending on your battery but you don't want to suck it all the way down).
If you're running a 60-watt light bulb for instance that's .52 amps on the AC side (60/115) and about 5 amps on the DC side (.52*10). You can keep that puppy going for 14 hours!
Hope this helps.
