Nope, it doesn't age you.
But, if you wear the wrong colors, especially of foundation, or if you don't wear any sun protection under it and your makeup doesn't contain any SPF, sure if you spend a lot of time under the sun eventually your makeup will enhance your wrinkles.
But there's not any direct link between makeup and skin aging.
I think this argument comes from a few decades back, with heavy foundations and son on. But it's no longer valid today, not with all the textures available, the SPF, oil control or moisturising properties of your foundation, the moisturising agents in your lipstick...
Makeup today is also a product inserted in your skincare routine, it goes with your skincare rather than work against it.