No they will not, explanation

[Horntail21]

It's precisely why the dragons we all get the most have the long breed times ie island,firestorm, coral, fruitful, poison. They aren't stupid. It's why they added the option to speed things up with gold. To make money! Something you jut gotta deal with.

[spiralraindrop]

They made it so that you can't cancel it (except with gold) because that's the point of the game. And yes, you're right, everyone would have had all the rare dragons by now. It doesn't make the game fun.