No.
It's because all the knights have tunics but not hats. Hense if TMC does come on the AT (which is pretty highly unlikely now judging by what we know from ST) the HoM story isn't a origin for hats, but it explains why he didn't have a hat.
Saavy?
^ There's actually an interesting theory about the tunic. It's possible that since there's a tunic and no hat, the HoM in TMC's BS could be some sort of knight in new Hyrule.
@Zemen: What's that? I think I see a Hyrule with all the old traditions coming back. :P
Jokes.
To elaborate on what SoJ said, the plot after PH seems to be as follows:
1. They find a land and name it Hyrule.
2. Some great demon king (Ganondorf probably) wants to take the land for...