That depends on the filesystem. If it’s a POSIX-compatible filesystem, then yes, although the permissions of files on the filesystem in question may then differ.
If it’s a Microsoft-style filesystem, then no, because they do not store or even understand POSIX permissions, and so the kernel has to emulate them in the virtual filesystem layer at mount time. As such, this means that the permissions will be set for the whole filesystem at once, not for individual files, and that you cannot alter the permissions while the filesystem is mounted.
More information can be found in the two tutorials below…
