well, sigle stage gen1 also has lot's of noise in low light condition, infact if you put a sigle stage gen 1 in test a chanber to measurement it's signal to noise, it will not give any result, SN of sigle stage gen1 in test enviroment (put 1.08*10^-4lux 2856k luminance in φ0.2mm area of photocathode) is less than 1. as i know this is because gen1 usually has very bad photocathode sensitivity in about 10-200μA/lm. so if you connect gen2 into gen1's screen, the perfprmance of whole tube will get worse.
early gen2 photocathode sensitivity is around 400-500, it can do much better to sampling low light signal. and after a gen2 tube intensify the light in it's screen, gen1's photocathode can be work in a much better condition, that's where gen1 tube can take advantage of it's low noise feature.
SN of image intensifier will dynamic change in defferent light condition and because there is no mcp inside gen1 ,the only noise source is photocathde and noise signal of photocathode basically just affect by temp, in low light condition useful signal become very low because of low photocathode sensitivity and noise signal unchagen, and electrostaic feild can't provide enougth gain to separated useful signal from noise signal.
E.G,for a gen 1 tube which has 100μA/lm photocathode sensitivity, a photon hit photocathode and emission an photoelectorn has 1.1keV energy, energy of electron emission by photocathode noise is 1keV , let's say feild gain is around 50, so useful signal after electrostaic intensify will be 55keV and noise will be 50KeV, 5Kev is theres defferent.
In gen2 tube, it has 400μA/lm sensitivity and emission photoelectron energy will be 4.4keV, noise emission is also 1kev. and hypothesis the MCP multiplication ratio is 500. ignore feild gain because double close gen2 basiclly has no feild gain. when the electron reach to screen, electron cause by light signal will be 500pcs of electoron with 4.4kev energy in each electron, which has 4.4*500=2200kev total energy, noise electron will be 500pcs of 1kev electron, total energy is 500kev, ther energy defference of noise signal and light signal will be 1700Kev, energy of light signal is 4.4 times of noise signal and 4.4 will be the Signal to Noise.