As long as you have the power pins on your riser, the factory PSU should support your Raedon's demands but you haven't given us your tower's Model # or spec sheet. Another option is to get a cheap PSU and run it divorced - i.e. outside your system's casing, powering only your card through a surge protector with a minimum of its' output harness.
As a rule, enterprise PC towers are overbuilt in these terms and consumer gear is built down to a price. That means if your tower is something along the lines of Precision, Optiplex, ThinkCentre, or anything "Pro", you're in the clear. The Pavillions, Inspirons, IdeaCentres, XPS's & Emachines of the world beg to differ - they're fire hazards unless they're closely monitored bulds.
It's not a tower (AIO actually) but I've got a fried XPS down for the count right now that's twice as nice as the Thinkpad I'm typing this on, it's just built like a Motorola RAZR whereas my Thinkpad is built like an automatic rifle. Impedences really matter - earlier this year I was working in 3D graphics and I learned the difference between DVI & DVI-D cables; DVI-D is a higher gauge because monitors over ~27" burnt through the insulation & desks.
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"Standing on a well-chilled cinder, we see the fading of the suns, and try to recall the vanished brilliance of the origin of the worlds."
-Georges Lemaitre
"I fly through hyperspace, in my green computer interface"
-Gem Tos
