Generally speaking with Quad Link SDI, the four SDI signals are expected to be genlocked (since they logically represent a single video signal), so it's possible that if you add additional hardware in the path of 1 of the 4 signals, this will add latency to just that one signal, causing problems with the video sync.
I'm not sure whether the Quad SDI to SDI 12G converter will still recognize the input signal as valid with this kind of configuration.