Something close to it, at least. I always felt like at the end of each stage, when it's talking about the Yoshis moving on that they sang "Be careful" over and over, almost.
Still, the game is notorious in describing how actual young Yoshis (not adult Yoshis trapped in eggs...) don't walk quite the same as the adults do, with a flatter back and longer neck, but rather straight upright. Luckily for those who liked controlling characters riding Yoshis, this wasn't something that lasted :)