I take it back. That UPS should be fine even with some upgrades. I just always go for the 1500VA model as it will normally cover everything on a standard US electrical outlet.
Apple's web site lists the Pro's power consumption -
http://support.apple.com/kb/HT2836
Mac Pro has a power factor correcting power supply so its watts and VA are almost identical under most loads.
I just did a few tests with a watt meter:
On my 6-core I see just over 130 idle and then 260 at full CPU load with the fans kicking in.
Sleep reads 5 watts / 16 VA - PF correction doesn't work that well at small loads.
Powered off reads almost zero - the meter doesn't handle it very well but shows there is some draw.
A 24" Cinema Display is reading a power factor of .55 - 25VA/14W (10/4.5 sleep)
So putting that together would still be less than 50% of the 800W of that UPS and run time on battery should be more than 25 minutes according to APC's chart.
Scanner should be OK but laser printers are not recommended to be put on a UPS.
If you do put two 5870's with 6 10K RPM disks then you might have a problem (and a problem with the Pro's power supply).
Also make sure it is the 120volt version if you are in the US. I see a lot of the 240v version (SMX1000i) on sale cheap.