Maybe I'm a bit 'old school', but traditionally, when shooting in low light situations you don't have to use ISO1600. You just need a tripod. But only if your subject is not moving.
Either way, even if you use a 5D II (or III for that matter), there will be some noise at ISO1600.
Going to a full frame body from the 400D will give you more bokeh (the blur from shallow DOF). You'll also be able to get more from the wide end of your 24-60mm lens, which isn't really a wide angle lens on a 1.6x body.
One of the downsides of going from crop to full frame is that you don't get to enjoy crop factor 'sweet spot' of your lenses. Most zoom lenses are nice and sharp in the centre, but at the edges they start to blur. With a crop body, the blurry parts are partially cropped out - but with a full frame body, you might get a bit of a shock to see what it's actually like at the edges. (Which might make you want to go out and buy more prime lenses!)
Other than that, you won't regret going for the 5D. If you ever happen to shoot sports or wildlife, you might miss the extra reach of the 1.6x factor, but just keep the 400D and use it for those situations.