Yes, you can choose to abandon a Faerie quest at any time, and you will not miss out on the final prize for visiting the event Hub Page each day. If you do abandon a quest, you will not receive another one until the following day of the event, when a new daily Faerie quest is given to you. If you abandon a daily Faerie quest on the final day of the event, you will not receive another; instead, you'll have to wait until a Faerie quest is offered to you through a regular Random Event.