Without having the exact specs of the PSU, it's difficult to give accurate advise, especially because we don't want to tell you that you can, when you probably really shouldn't.
I did find an article here;
http://compreviews.about.com/od/maindesk/gr/Dell-Studio-XPS-8100.htm
which states, "Graphics are probably one of the weakest aspects of the Studio XPS 8100 system. The main reason for this is the relatively small 350 watt power supply that lacks much of the performance needed for the high end 3D graphics cards. The default NVIDIA GeForce GTS 240 graphics card provides a mediocre experience with support up to 1650x1080 resolutions. Those wanting higher graphics will either have to upgrade to a GTX 260 for 1920x1200 support or a Radeon HD 5770 for Direct X 11."
According to AMD's website however,
5770:
http://www.amd.com/us/products/desktop/graphics/ati-radeon-hd-5000/hd-5770/Pages/ati-radeon-hd-5770-overview.aspx#3
"450 Watt or greater power supply with one 75W 6-pin PCI Express® power connectors recommended"
6850:
http://www.amd.com/us/products/desktop/graphics/amd-radeon-hd-6000/hd-6850/Pages/amd-radeon-hd-6850-overview.aspx#2
"500 Watt or greater power supply recommended"
Now, obviously, people have put 5770's in the XPS 8100, which does not meet AMD/ATI's minimum requirements for the 5770, and it seems to work fine, but it's pretty clear that the 6850 does take a bit more power, which would take that poor Dell PSU one step closer to the edge.
It's all your choice, and I stand by the "without knowing the PSU's exact specs" but, personally I wouldn't go against the hardware manufacturers specified requirements.