If I get an NZXT s340 and an Enermax ETS-T40-W how big a gap will their be between the gpu and Enermax ETS-T40-W? Will it be enough to see the GPUs backplate fully?
The case has nothing to do with it. It depends on the motherboard. It should work fine, that cpu cooler is not very big, about half the size of the real big coolers.