My Dell PowerEdge 2850 is similar and I wanted to install an HD 5770. In the PE 2850 the dual power supplies are hot swappable.
What I had to do is bust out my volt meter and perform a little surgery. The hot swap power supply had some even number of power takeoffs. With some testing it turned out that I had +12v rails and ground rails. No +5v rails, but that's OK since the 8-pin adapters want +12v.
What I did then was map out the electrical connections required for the 8-pin adapter, and soldered the appropriate wires to either the +12v or ground. It actually wasn't that difficult once I got over the fear of performing the surgery.
So it can be done, but this approach is not for the faint of heart.
One other consideration is the PCIe bus bandwidth. On my server it's only PCIe 8x. Some research I did awhile ago told me that anything more than an HD 5770 might saturate the bus and provide diminishing returns, YMMV.
Finally, in Dell's case, I ran into a situation where Dell may not actually provide the full 75 watts to their PCIe bus. Check your server specs carefully to see if HP gives you what you are expecting.