Most likely yes. In fact they make reference to Andy Diggle at least once. They refer to John Diggle's deceased brother twice in episode three. Once in a conversation between John and his sister-in-law where they do not actually mention his brother's name, and once while Deadshot is tattooing himself, the name Andrew Diggle is shown tattooed on Deadshot's chest, implying that he may have in fact been the one to kill John's brother.
In the show, John Diggle's brother is named Andy. Contrary to what the other answers say, Andy's name has been mentioned numerous times by John and even Lawton. Lyla even mentions him by name a couple times, as well as Carly. But to answer your question, yes, John Diggle and his brother's surname is a direct reference to the real life Andy Diggle.