Nah, the outer layer of the flexible screen is quite rigid to the touch. You don't leave marks with your fingernail. I've used TPU screen protectors on the inner screen that have that property, I think. If you look at the glare from a light source, you can see indents in that. But even then, it's not something you otherwise notice.

I don't want to seem like a breathless booster for flexible phones, they are too expensive to be considered practical, I think. But there are some misconceptions about them, some which seem to come from the first version of the Z Fold, which honestly does sound like a nightmare device.