Yes, I myself always play d5 in Nimzo, and c5 if possible. But you usually don't move pawns in center right away, which is typical of hypermodern openings and is also part of Caro-Kann, where you play c5 much later. Caro-Kann really seems a bit of mixture of hypermodern and classical openings to me.
Edit: Rooperi, Polish is considered an "irregular opening". But so is the Zukertort, which is hypermodern. I think that a "flank opening" is a better name for 1.b4.
What about the Polish? Is that hypermodern?
"and we all get put in boxes, little boxes, all the same"