after 15 adventures on both Queen's court and Barracks, I got only one pyre egg. (it was out on 5th try) so I decide to skip for sparkling egg first. (and tomorrow or later i will skip for ultramarine egg, too. because i'm really busy now due to my baby's fever.. and i'm so tired to challenge this event.. ) I already spend almost 100 gems to get armor for pyre cavern directly.. i think that's enough for me. no more mithrills to make ice brand... omg 1 mithrill for 50 gems. )
so yes. if you skip, you will get one egg in your inventory.