Does the sex of main character influence the game?

There are two perks that are affected by your interaction with the opposite sex:

1. The Allure perk in the Speech tree, which Xenox mentioned, that gives you 10% better prices with members of the opposite sex.
2. Completing The Heart of Dibella will grant you the Agent of Dibella perk, which will give you a 10% melee damage bonus against members of the opposite sex.

Yes, it does. For example, there is a perk (Allure) which decreases the price of items when trading with persons of the other sex.