Absolutely not. Fanout has nothing to do with timing."

Actually, that's not true. Consider fanout being the capacitive loading on a signal. Increase that loading, and you increase the time to charge that capacitance, which ultimately affects how fast you can toggle that signal.
1) fanout is determined by the DC characteristics and thus capacitance has no bearing. Your statement about capacitiave loading is correct, but does not relate to fanout.
2) If your "fanout" is low due to capacitive loading you will have a heap of other problems.

Erik