The installer filesystem should be an initramfs, so it should all be in RAM and writable (at least in the netboot case, but I don't see why CDs would do it differently; I expect the extra storage is just used for packages), at least for d-i stuff.

Even for proper (not install only) live CDs where the rootfs is really read only, I don't think I've ever seen a distro not mount an overlayfs on top so that changes can be made in RAM. Too much stuff breaks on your average distro if you really try to have a read only rootfs.