first off a 600va unit can handle about 350 watts. a 2010 6 core pulls that much wattage routinely. So the answer is no the unit is very under powered so much under powered it will do more harm then good.
Here are the technical specs for your pick pulled from your link
OverviewDescriptionTechnical specificationsSupportUPS 600VA
EM3980
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Capacity: 600VA or 360W >>>>>>>>>>> See only 360 watts far under powered!!!!!!!!!!!
Input voltage: 220 VAC ±25%
Input Frequency: 50 Hz±5.0Hz
Wave form: modified sine wave >>>>>>>>>>>>> pure sine wave is considered to be better!!!!!
Battery: 1x 12V 7Ah
Backup time: 10..15 minutes for 1 computer
Recharge time: 8 hours (90% charge)
Transfer time: less than 10 milliseconds
Surge protection: 320 joules in 2 milliseconds
Software information: frequency, input-, output-voltage, load, battery capacity, status and temperature
A few questions You gave price in euros That make me think you don't live in the USA. It helps to know the country you are from. We have worldwide posters so if you are from the UK a UK poster may know a good deal. So what country are you in? Next question is do you use the pro for business? If you do a ups is more important then if you are a hobbyist.
if you have a 6 core you need a 1200va or a 1500va machine . if you lived in the USA I would say get this:
http://www.vanns.com/shop/servlet/item/features/753163336/apc-s15?s_c=site_search
A really really really good deal. At 300 USD it is half price. It has a pure sine wave. I do not know a UK equal but I am sure a poster will give you a few good uk deals.