Answer
This heuristic will not always work.
Work Step by Step
Consider a network having 4 nodes a, b, c and d. Suppose b is closest to a, c is closest to b and a is closest to c, in this system a b and c will form a cycle and any node from a, b or c will never be able to reach d because if will always be stuck in a, b, c cycle. Hence on networks like this the heuristic will not work.
