I was not aware that radiators made noise. If don't think it's a big deal really, but that is just my opinion. If you have a baseboard radiator heating system, sometimes they take up so much wallspace, it's hard not to put a tank near one. However, in a baseboard heating setup, the heat is spread over quite a wide area.
If you have one of those more old fashion radiators that are much larger but only a few feet long - they can put off a lot of heat in a smaller area. I would think that a tank to the left or right of one would be OK. Obviously I wouldn't put a tank on top of it. If the tank is in front of it, then the whole length of the tank is exposed to the heat, that might affect the temperature also.