The Canon 7D MkII is definitely less noisy than the Canon 600D. Take a look at this comparison in good light with both cameras at ISO3200. The comparison is actually between the 7DmkII and the 7D, but the 600D has the same sensor and processor.
Based on this comparison the 7DmkII is obviously better in noise terms and further having also played around with the image parameters in the test image I would say that you could think of the 7DmkII as having approx 1EV (1 stop) less noise than the 7D (600D equiv), in the sense that the 7D at ISO 1600 has similar noise to the 7DmkII AT ISO 3200.
So you'd get an improvement (reduction) in noise by going for the 7DmkII,
but it wouldn't be as great as the reduction you'd achieve with Bojan's suggestion of removing the IRcut filter in the camera, which would increase the Ha response by a factor of around 3 and thus the signal to noise by a similar amount. Net effect less noise, because you would have to dig down less in to the signal (stretch). ... And you have a lighter camera than you started with - well a few grams lighter anyway
If you are concerned with the camera being no-usable for normal photography well that's one thing. If you are concerned with too much red, then there's always the ability to reduce the red channel saturation in editing or boost the other channels after the fact.
Best
JA