The brake cleaner is nasty stuff. I love using it when I work on a car. I used a whole can to clean out a fender well that was full of axle grease from a broken boot. It burns like gasoline on your skin, only it starts burning about 10 times faster. This can't be a good indication. I won't get this stuff near my bike.
Aren't some chains lined with plastic or teflon? If so I wouldn't use much chemically stuff on them either. I would put my chain in my parts cleaner but I don't feel like taking it off. It's full of automotive grade solvents. The can said not to leave aluminum and plasitc in there for too long. "Where did my cassette go?" It will dissolve rubber.
I would do the simple green thing or the citrus thing if I did this kind of maintenance. My riding has been ramping up more and more so I need to get one of those chain/geary washy thingys.