I guess it might be able to under regular gaming, when the graphics cards aren't drawing their theoretical maximum and not all the CPU cores are loaded, but anything that fully stresses that system will surely be too much. 4 GTX480s in Furmark will break 1200W on their own. In that system, with the power hungry motherboard, cooling and CPUs, a 1200W PSU might not even sustain 3 480s. On the other hand, perhaps that PSU is capable of delivering beyond its advertised peak. You could look at mounting a 5.25" bay secondary PSU somewhere, which could power all but the PCI-E slot demands of the 480s. That'd leave you with about 750W being demanded of the 1200W PSU by the graphics cards, leaving 450W for the rest of the system, which might be enough depending on your overclocks.