Well i can answer half your ?, a 1000watt yes if gonna be the best for a GTX 580 SLI setup. anything bellow 1000. you asking for trouble. as for the UPS thing, i havn't used a UPS yet so i wouldnt know
As for a 750w psu running 2x gtx 580's I'm not completely sure. When I was running 2 my wattage load was between 450-600 watts with a slight factory overclock though I was using 1250w enermax psu at the time.
As for the battery back up, I recently upgraded my psu to an AX1200 when I recieved my 3rd 580 and I noticed in the manual that for a 1200w psu it is recommended to run at least a 1500w ups.
Honestly I was running a 900w ups with a 1250w psu for 2x 580's for almost a year, and though I ditched the ups when I got the third card I'll be willing to bet you could make your setup work as long as it is one sweet 750w psu. I'd have to say I wouldn't recommend it though. If the strain of the cards overworked the psu there is a chance of a surge ruining your gear.
it all depends if the psu is from a good brand, some brands sell 750watts but offer at max 600 ... a lot of this happens, and good brands with 750watts they can 800 even 900 w, so what is your PSU? look some stress tests realized on it and see what is the maximum it really can handle.
if it can keep 750watts real so i think yes you can try SLI but stock voltages, no overclock neither in cpu/gpu...
about the UPS i'm not sure if it is recommended to use such things, i know that line filters and stabilizators just lower psus efficiency, so better to turn it on directly on the energy;
Step one is to figure out the wattage of the 580, specs say its max draw is 250. So your two 580s will draw 500 watts. That leaves on 250 for your board and chip. It should work ok but your cutting it very close.
Second thing to look at is the amperage that the 12v rail of the PSU can put out. Finding the amperage of the GTX580 is not easy because the manufacturer does not always publish it. Reveiws I red put it between 25-30 amps. So you need an amperage of 60-70.
Unlikely you will find a 750 watt PSU with that type of amperage. You will probabbly need a 850 or greater.
Finally question about the UPS. The Voltage amperage of the UPS is not as important as the wattage. An easy way to look at it is, the PSU can supply 750 watts of power to the PC but because it is not 100% effecent it can draw up to 10 % more from the wall, so your 750 PSU can draw 825watts. So your UPS must have a wattage of 825 or greater. The UPS voltage amps should be at least 20%-40% greater than the wattage, so an 825 wattage UPS should have a Voltage Amp of around 1000va.
what's your total system specs? and why do you need the UPS?
System power consumption with 2 GTX 580s in full load consumes 720W so yes a quality branded 750W PSU will handle the 2 GTX 580s, but you will be in a real problem if you're going to be OCing. In this case a 800-850W PSU is what you need.
If you know the max watts that a PSU will draw and the voltage level, then you can easily calculate the amperage. Amps = Watts / Volts
So a single 580GTX with a max 250W load is equal to 20.83333333 amps.
Two reference clocked GeForce GTX 580 in 2-way SLI mode will draw 37 Amps from the +12V rail(s) for the two graphics cards only.
You never specified the rest of your system configuration like the all important CPU which also gets all of its power from the +12V rail(s).
A 750 Watt power supply with a combined +12 Volt continuous current rating of 55 Amps or greater and with at least two 6-pin and two 8-pin PCI Express supplementary power connectors would be enough to power the system.
I'm still thinking what case to buy so I don't know how many fans i'll be running, i was thinking in a CM storm eforcer, a HAF or a elite 431plus
I believe I need the UPS because the power here is a bit unstable, my actual surge protector blinks when loses power from the wall for a milisec and shuts down my actual pc... maybe If I buy a more powerful surge protector instead the UPS ?
I'm not sure if it's safe to plug it direct to the wall...
And about the SLI I tested some online calculators and says it will need a 735 watts psu but I'm not really sure, I would like to run it for some months till I can upgrade it I didn't expect to get a second 580...
There's a way to check if the PSU is doing well while using the SLI in a game ? like the wattage and amp use with any software or tool?
$1000 worth of gpu in a 431($50)case lol!
You might want to spend $100+ on a case with plenty of room and airflow.
At least a HAF 922 = 932 Advanced or X would be better.
And you might want to get an 850W psu for the difference in cost of a 750W.
I know i would.