Yes, Coleman did threaten to sue the creators of the show due to the fact that he didn't like how his character was lampooned. However, I don't think that went very far though.
I had always thought that the name change to simply "Gary" in the London production of the show was simply because the creative team wasn't sure if the whole ongoing Gary Coleman joke that is used in the American production is something that the british audiences would get. Only to put the name back in as Gary when they were wrong. Didn't they originally call the character "Job" in the London production?
"If you try to shag my husband while I am still alive, I will shove the art of motorcycle maintenance up your rancid little Cu**. That's a good dear"
Tom Stoppard's Rock N Roll