The 700 W rating is the maximum load that can be used from the UPS without any damage to it, or it with it being over-loaded. Normaly, the maximum load should not exceed about 60% of the maximum capacity of a UPS.
In the instruction manual for the UPS, they usually give a chart of how long it will supply power with different loads. The effect of the load may not be exactly linear because the load is being run from an inverter. This inverter itself uses a certain amount of base current to operate. It's efficiency may not be very linear.
In theory, a 120 Amp Hour battery should be able to put out 120 Amps for one hour. Normaly, when a battery is under load, when the voltage of the battery has decreased to about 10% below the nominal rating of the battery voltage, the battery is considered weak.
When evaluating a battery, make sure that you know if the Amp rating of the battery is the maximum output load, or it is the maximum Amp Hours. There will be a difference in its performance.
A standard 12.5 Volt battery would be considered discharged when its output has decreased to 11.36 Volts. This is when the battery is under its nominal rated load. For most gel and lead acid batteries, the maximum normal load is considered to be 1/4 of the Amperage rating of the battery. This would be the load rating best for testing the battery, and for having the most efficient use from it.
If you have a battery rated at 120 Ampere hours, in theory it should be able to put out 120 Amps for 1 hour. In reality, if you did this, the battery would be under severe stress. A 120 Ampere hour battery should be able to operate a 10 Ampere load for a period of 12 hours.
In a UPS, there are a number of electronic circuits that have to be operated by the battery. There is also the inverter output driver itself. These all consume some of the battery power. It may be as much as 10% of the available power when it is on the battery.
A very simple example of evaluating a UPS would be to look in the instruction manual. If it indicates that the UPS can run for 15 minutes at the full load, then it should be able to run for at least 30 minutes at 1/2 load.
In calculating your load, you are asking about 600 Watts from the UPS. This is about 90% of its load capacity. Without the internal load of the UPS's electronics, this works to 50 Amps at 12 Volts for the battery. If I add 5 Amps for the electronics, I get 55 Amps. If the battery is rated at 120 Ampere hours, you should be able to get at least 2 hours of operation.
Personaly, I would not share the same power source for a computer with other appliances, and especially if they are reactive devices such as with a motor. The only thing I would have on the UPS is the computer, the monitor, and the printer if the UPS can take the load. For lighting and the extras, I would use a separate UPS.
For the emergency lights here in my office, I have a 1200 Watt UPS running a few compact fluorescents with a total of less than 40 Watts. With the battery power I have with it, this light will run for over 24 hours.