I'm working from memory here, not having had anything to do with a Bloodnot for about 9 years, but yes, the FI is a more refined equivalent of airframe hours, which takes into account useage (i.e. more g = more index accumulated).
It doesn't replace A&E hours, so much as supplement them for fatigue critical components such as the mainspar.
That however is about the limit of my memory, if I needed a clearer answer (which you probably do) I'd go and speak to dHSL - de Havilland Support Ltd at Duxford, who hold the Type Certificate for the aircraft and should be able to give you chapter and verse.
G