If there are any characters faceup in a province but not in play (i.e. still sitting on top of the province card) at the beginning of the fate phase would they be discarded due to not having any fate on them?

Rules Reference Guide, page nine, In Play and Out of Play.

"Out-of-play” refers to all other cards and areas involved in the game environment, including: character cards in a player’s provinces, role cards, cards in a player’s hand, decks, discard piles, and any cards that have been removed from the game."

Fate is only removed from Characters in play.