It is sufficient. A system with a single GTX 670 requires a PSU with at least 38A on the 12V rails and two 75w 6-pin PCIe power connectors. A system running a single GTX670 and a highly overclocked, power-hungry i7 965 used 279W at full load: http://www.guru3d.com/article/geforce-gtx-670-review/8
The GPU wasn't OCed, but you probably won't hit 350W even with OCs on the GPU/CPU. You're won't hit the power consumption of the i7 they're using in the review. Combine that with a moderate-high OC on the GPU and 350W isn't likely.