Simple answer is NO, your Crossfire will be slightly crippled- as to how much, maybe not a lot. For a definative answer you'll have to search for Motherboard/Crossfire (and SLI) reviews based around a PCIe x16, PCIe x4 board such as:
Giagbyte P55-UD3R/-UD3/-UD3P (and the P55A versions), MSI P55-CD53, ASRock P55 Pro/P55DE/P55DE3 Pro, Asus P7P55D/ P7P55D LE, EVGA P55 LE and any AMD boards (sorry, I'm lazy and AMD chipsets hold no interest for me).
As for power supply AMD recommend a 600 watt for Crossfired HD 5770- that seems a little overkill since the cards are TDP rated at 108 watts each. ASSUMING that you aren't running a massive overclock and have a usual setup ( 1-3 harddrives, 1 or 2 optical drives and some USB peripherals and case fans) then a GOOD (branded) 520-550 watt would suffice. As with any system- buying a piece of crap cheapo psu is a quick way into trouble. Stick with a good a brand: Corsair, OCZ, Enermax, PC Power & Cooling, Silverstone, Gigabyte all make well regarded PSU's, while certain models within the Thermaltake, Antec and Cooler Master lines offer a good alternative.
BTW : Why Crossfire HD5770 over a single HD5850 - surely the single card is cheaper, and offers better performance.