What you are thinking of operates at a different level of abstraction. Energy functions are a general way of structuring a problem, used (sometimes abused) to apply an optimization algorithm to find a reasonable solution for it.

FAST is an algorithm for efficiently looking for "interesting" parts (basically, corners) of an image, so you can safely (in theory) ignore the rest of it. The output from a feature detector may end up contributing to an energy function later, directly or indirectly.