Generally a 680 takes 2x 6-pin and 550w, so theoretically yes, it'll work. However, I don't know of any 550w with a dedicated 8-pin pcie, but I know of several cheapo 550w that have just a single 6-pin, but include an 8-pin EPS, which is not pcie. Is it an 8-pin?or 6+2-pin? Not all 550w are built the same, there's many that are really 250-300w psus in disguise as a 550w. Quality in this case counts more than quantity.
That said, there are mitigating factors. Some few gpus have added power requirements, so might demand a 6-pin and 8-pin, or have a different power delivery setup, so might only require an 8-pin. Depends entirely on the specific gpu.