I agree it should be fine too - but the bond from synthetic to carnuba won't be as good so it probably won't last as long - also NXT has very mild cleaners in it so it will remove some of your gold class as you apply.
If it were me i'd wash it with NXT shampoo, quick clay then NXT follwed by another NXT 24hours later.
Although it works washing up liquid can cause other problems else where on the car - ie greased joints etc!