Can this cake be made without the candied oranges?

Absolutely! Feel free to skip the oranges, top the cake off with some powdered sugar and you should be good to go!

The recipe writer says in the intro that the cake initially did not have the candied orange top, and was meant to be simply a cardamom olive oil cake. Since the oranges themselves serve only as a topping to counter the cake, I don't see why they couldn't be omitted.