That’s quite a combo. The satire comes enters into Fitzgerald’s not-so-veiled critique of society. He exaggerates Mr. Button’s obsession with keeping up appearances and hyperbolizes the omnipresent fear of what is different. The whimsical fancy is pretty clear, too, as is the humor, from the moment we see Benjamin, "a baby of threescore and ten" with his feet hanging "over the sides of the crib in which it was reposing" (1.1.39).
But there’s a real poignant element to be found here as well. You’re bound to feel emotional at Fitzgerald’s description of the aging Hildegarde, "devoured already by that eternal inertia which comes to live with each of us one day and stays with us to the end" (1.7.7). Now there’s the Gatsby-writing Fitzgerald we all know and love.