Connex links are easy to undo, they must be put on the correct though to avid an unintended delinking. SRAM links are easy to undo if a bit stiff, just use pliers with the link placed diagonally in the jaws. No need for a specialist tool you'll be lucky to use only very occasionally.
I used to be a chain dunker to clean, even ultrasonically cleaned my chains. So clean you could almost eat of them. But that shortens the life, the good original lube which is largely unaffected gets cleaned away accelerating wear internally. Nowadays being a mostly SSer, I just wipe chain, relube with my personal favourite which is a blended formula and works very well.
As for the original question, yes you can clean on bike, be careful though as any solvents that get around to unwanted areas can affect your maintenance of other parts of your bike. Things such as wheel bearings, pivot points on derailleurs, jockey wheels are just some immediate areas to be wary of.
