Will an UPS use its power supply all the time?

The UPS usually detects power from the AC wall outlet and bypasses (if the battery is charged all the way). Then when power goes down, UPS detecs it and kicks in the battery power.

It depends on what UPS you purchase, most of the cheaper UPS's are line-interactive meaning that it uses a Autotransformer that switches voltage as it see's fit depending on what kinda power is coming out of the wall outlet. With this one it runs on A/C power via the wall when it detects overvoltage/undervoltage it makes up for the voltage with a transformer instead of using the battery at any time it detects a power fluctuation unless it's a really big spike or complete AC power loss then the battery will intervene.

Here's a visual to better understand



There are double conversion UPS's that filter all output power through the batteries first. This is the best protection but the most expensive.

So to answer your question your computer will draw AC power from the wall and switch to battery power when needed(unless you have a double conversion UPS)

Thanks Orlean. Forgot to add the part about depending on the quality.  

My pleasure   I just recently purchased one myself so I was doing allot of research regarding UPS's.