Offspring from Zinnia+"enter as a copy"

Suppose I have [[Zinnia, Valley's Voice]] in play and cast a [[Clone]]. When I cast the Clone it has Offspring and I pay the {2} but does it still have offspring when it enters as a copy of something that doesn't have it? One of the rulings for Zinnia is that if it doesn't have offspring when it enters it won't create the token. If it doesn't work for Clone, is it any different for [[Sakashima of a Thousand Faces]] who keeps his abilities when copying something?