Eliminating Signal Race Hazard in an IC dynamic latch/register!
Yes, if you replaced the NMOS transistors with full transmission gates, where the P and N transistor are on opposite clock phases, then you will have a race problem. Suppose your two clock phases are named PH1 and PH2. One of the transmission gates should be controlled with PH1 and ~PH1 and the other should be controlled by PH2 and ~PH2.

You cannot use PH2 as ~PH1 or use PH1 as ~PH2.

You must verify that the non-overlap condition still holds for the inverted phases as well as for the true phases. If you need to increase the non-overlap, add pairs of inverters in the feedback paths of the cross-coupled NOR gates.