Dear,
very interesting question. Very often the consulting world is seen as a unique domain. It's not. Consulting is a general word that comprises many nuances.
In your case, I can tell you that the role of a functional analyst is very different from the role of a management consultant. The type of activities and output you'll be required to deliver differ from what you'll be asked as a management consultant. In my consulting experience, I often time worked hand-in-hand with functional analysts from other consulting firms because the scope of the project required different skills and competencies.
Trying to stay practical, working as a functional analyst can certainly teach you a lot but it is not a conditio sine qua non for increasing your chances of being a management consultant in the future.
I like to view this case with a metaphor. Think of a restaurant. For all roles within the restaurant, the goal is for the restaurant to be successful and busy. However, the responsibilities of a waiter are very different from those of a chef just as a sommelier has different skills from the restaurant manager.
Therefore, I would favor a work experience in management consulting to stay consistent with your end goal.
However, as always, there isn't a single “magic” path to reach the ultimate goal. And very often achieving it is the result of determination and individual choices (and a dash of luck). I know many examples of colleagues who started out working in totally different consulting fields and ended up working as strategy consultants at McKinsey.
Feel free to DM me to discuss this interesting topic further!