Yes. The Hero does get the benefit, such as gaining a Fortune, for the initial skill gained at the start of the game. So the Hero might actually have 6 Fortune at the start of a Story card.
Check out the side bar in the rule book (pg 8):
Fortune from Skills & Quests
Certain skills and Quest cards give Fortune when
learned. If these Fortune are gained just before a new
Story or Final Battle stage, the player gains these
Fortune in addition to the normal 5 Fortune a player
starts with during the Preparation phase.
Example: If Seroth learns the first level of the “Titan”
skill at the beginning of the game, he will start the first
Story card with 6 Fortune to spend.
Hope that helps.