Boy Mulcaster is essentially an ill-mannered rich kid. When Anthony tells the story of him and his friends in colored tailcoats threatening to throw him in Mercury, we know that Boy has just come from some pretentious dining establishment, is now drunk, and is terrorizing the campus and causing trouble. Anthony quickly fills in the details when he tells Charles, "If you want to know what a real degenerate is, look at Boy Mulcaster." It seems that Boy, who is apparently a British Lord, made a general fool of himself while staying with Anthony as a guest. Anthony’s opinion of Boy is confirmed when we see him pull a fire alarm at a crowded nightclub because he simply wants to "cheer things up." It just goes to show that being from the upper class doesn’t necessarily mean you have any class.
And aside from that little platitude, Mulcaster simply serves the plot purpose of bringing Celia into the picture for Charles to eventually marry.