Power shuldnt be a problem if its not a noname 20gram unit ...i run quad q6600 + HD 3870 +5 HDDs with 550W LC power ..
But as mentioned above ..why for christ's sake do you buy an x1950 pro in the age when a low price HD 4670 wipes the floor with any x19xx ..heck ..even an 4830 can be had for below 100$ mark ....i'd definitly go for that ...
Even if it's a no name unit it should be O.k as long as it has enough amps on the 12v rail. If it has something like a single 15A rail then it's not going to be enough. Well it will be enough to boot but running games will either activate the trip protection and shut to machine off or just fry the system. The minimum you should go with is something with an 18A 12v rail or 14A dual 12v rails. Even then that phenom based CPU uses alot of juice so if your PSU is in that minimum you would be safer going with a 5400 BE that uses a bit less power
You also have to consider that if it's a no name unit it may only be able to support 18A as a peak but not really sustain it. It just depends. I'm assuming you are already using a 1950 Pro and that your system can handle it with your current configuration, in which case you should be safe and your PSU should be able to handle the CPU and motherboard upgrade. If you are going to buy a 1950 pro though I would say don't. Consider getting a 4670 instead which uses alot less power and is much faster (between 40-100%) .