Just so you know the GX 650 is a very low quality PSU, coolermaster is a mix of good and crap, it's not a coincidence that it's way cheaper than other 650W PSUs. 5830s are the next most intensive consumer of electricity after the 5870, and I'm not saying they won't run on that PSU, but I wouldn't use it myself. It might not explode immediately, it might not explode ever, but there's a reason why people spend more on what is arguably the most important single part in a computer (especially one running hot 24/7).
The raw answer to your question though is yes, 650Watts will run 3 GPUs assuming a small enough system and little to no overclock on 5830s or below.
Thanks for the detailed reply. I bought the GX 650w specifically because I thought it was the best priced PSU for the quality. I know it's not the best, but it seemed like a suitable medium between the poor generic PSUs and high end Corsair style PSUs. I just wanted something reliable. I'm not planning on overloading it so I think it'll be fine. As for the 5830, that's true. I'd probably prefer a 5770, but it depends which card offers the best price/performance, which is pretty much what i've aimed for in my entire rig.