How long will a 2.0 amp draw last on a 400 watt battery back up system. UPS  ?

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Since UPS usually outputs 110 volts, a 2 amp draw will dissipate 220 watts/Hr. Depending on the model UPS it might have a shut off point where the battery has been drained a certain amount. The device needs to use power itself, so the device it's powering isn't the only drain on the internal battery. Read the instructions that come with your UPS and it will tell how to calculate how long the UPS will run. When in doubt, do a backup and shut down to avoid data loss or device damage when power fails and the UPS takes over.

If Output of UPS is 117 volts, in theory,   1.7 hours or  1 hr, 42 mins.

 If output is 234 volts (Europe), about     51 minutes.

This is assuming ideal situation, batteries  good,  the 400VA rating is for one hour. Not a 3 or 10-hour rate (I doubt this, I 've had two).

EDIT: Most  larger UPS' use 48 volts, total, in the battery complement. Usually means, Four 12-volt gel-cells. You'd need  Four standard 12 bolt car batteries. (some pickups are 24-volt), and, unless  sealed, can be hazardous inside a dwelling, yes. At Least put them in a plastic tray and run a fan that uses a synchronous motor (no brushes-!!) to help vent gasses.

Not enough information with your question is provided. I wouldn't recommend putting a car battery inside your house if that's what you're doing. Unless the battery is NOT being charged or discharged and it is safely being stored.

I'm an expert and there isnt enough information. What voltage is the battery? What voltage is the draw? What kind of battery is it? 

Also batteries have what is known as a "safe depth of discharge". Lithium phone batteries can be 90% discharged without hurting them. But lead acid car batteries shouldnt be discharged below 50% capacity. 

Etc etc etc

Not enough information.

About an hour and 45 minutes.