I've been using it for years to clean the bike with no problems, but not specifically for the chain. For that I ususally use a rag soaked with chain lube and rub the hell out of it (I don't let my chain get too dirty anyway, though). Simple green probably won't mess up the o-rings any worse than a high pressure water jet rinse. I say use it to clean the bike, but give the chain a bit more TLC and avoid direct spraying with water which could force moisture past the o-rings.
this topic will bring nearly the debate that oil does. If left on aluminum it will corode it, so make sure you get it all rinsed off. I wouldn't get it anywhere near my chain, but that is just me. wd40 or kerosene work fine.
Kerosene (or lamp oil, same thing, less smelly) is the best thing to clean the chain with. Then something like Maxima chain wax or PJ-1 chain dressing to protect it. Kerosene also is the best thing to clean the wheels and sprockets with. Safe, cheap, quick.
You can use Simple Green on everything else, just be sure to rinse it off well. As stated, you don't want to leave it sitting on aluminum and you don't want to use it on hot surfaces. On a cold bike, spray it on, wait 10 minutes, hose it off. I use it to get residual kerosene off my rear wheel after cleaning the chain and rewaxing it.