Yes, an OC'ed 1080 (depending) will probably pull more power from its single 12V-rail than healthy, and would need the second 12V-Rail, thus leaving no free connector for the 1060. Two 1080 in SLI reqires a 850W PSU (as recommended somewhere on Toms Hardware), so, if you subtract the typical load of a 1060, this means 700W for *normal* 1080 + 1060. But under normal, non-OC'ed circumstances, unless you drive a furmark on both GPUs at the same time (unlikely), the 600W may be enough. But with OC coming into play, this may easily get out of hand.
Mark it, the problem is not the combined output, but the ability of a single 12V-rail to provide enough power for the card.
But maybe ask others as well, mine is just one opinion, and a new PSU is...