No, side accounts cannot participate in this event. Since the Faerie Festival event - where you receive a "free" guaranteed faerie quest every day - gives out extra daily rewards, it is treated like any other event. You may only participate in Faerie Festival faerie quests on your main account.
This is different from regular faerie quests that are given out in Random Events; you may participate in those on your side account(s) if you happen to receive one, so long as you earned the NP for the requested item on your main account. (Remember, earning NP or items on side accounts isn't allowed.)