It depends on how acoustically similar the pads are to what you're replacing. For instance, my K702 is equipped with Dekoni earpads, and those earpads were designed to be as acoustically similar to the original pads as possible, and they provide frequency response measurements of original pads vs. their pads, and I can confirm that yeah, their K702 pads sound basically identical to the original pads and I couldn't detect a difference.
Then there's the other end of the spectrum where you can fit completely different pads to a headphone. Like the Koss KPH30i with Grado G pads:
I've done that myself and the difference is 100% night and day. Not even slightly subtle. Dramatic change in sound.
So at one end of the spectrum you've got pad options that try to preserve the original acoustic properties as much as possible, at the other end of the spectrum you've got Frankenstein mods where you've got pad/headphone combos that were never designed to happen and produce wildly different sounds. And then in between those two extremes you've got a whole lot of grey area where maybe the pad/headphone combo you try influences the sound in a subtle way, or maybe a not-so-subtle way, and sometimes the changes are for better, and sometimes the changes are for worse. For instance, in my experience AKG headphones are very picky about earpads and nearly every aftermarket pad I've slapped on an AKG just sounded worse. The only exception being the K702 and Dekoni's pads that were deliberately designed to be as similar as possible to the originals.
I've also tried some Audeze earpads on an Audio Technica headphone of mine and the bass turned into a giant boomy bloated mess and it just totally destroyed the tuning, couldn't stand it. But then you've got headphones like the JVC SZ2000 which is basically the dullest headphone on the planet, until you slap some aftermarket pads on it like the Dan Clark Alpha pads and suddenly the headphone positively comes to life, literally sounds like a completely different headphone. Absolutely incredible improvement, leaps and bounds ahead of the stock pads.
In short, can different earpads dramatically change the sound of a headphone? Absolutely, 100%. I've experienced it many, many times. Will pad rolling always dramatically change the sound? No. Like all things, it depends. But yeah, if you want to have a fun, inexpensive experiment, the KPH30i + Grado pads as shown above would serve as a great demonstration of just what kind of transformations can be achieved by simple modifications.