I presume by "generic" you mean "regular adventuring characters in any genre: space, fantasy, crime fighters, World War II, etc." My first thought is "Yes, you can." But then... why would you want to? You would immediately run into problems that other systems already solve.
For example, the issue of skills. In virtually all systems skills are an important part of characters and how they are played. What skills a guy has, at what level of proficiency, etc. In Amber skills are mostly hand-waved, which seems fitting for characters who can be hundreds or even thousands of years old. You want 5 Doctorates and 10 Masters degrees? Fine, you got them. You want a guy who has been a General for 100 years and a leader of an empire for 200? Fine you got it. See what I mean? If you wanted to play with more normal characters though you would have to put in more definition, more limits.
Then you have to change the combat system. When dealing with powerful and well-aged characters the Amber system of Warfare and Strength and Endurance is fine. But with closer-to-normal people I don't think it would be satisfactory. Random elements and "accidents" can have a bigger effect. In Amber a 40 Warfare guy will, in theory, always win over a 20 Warfare guy. With more regular characters... no. A minimally trained guy won't win a contest against an expert but he can get lucky and defeat the expert randomly. Children shoot and kill adults, a street thug can plug a cop, an idiot-terrorist can spray bullets and kill a couple professional soldiers, etc.