Pipes lack a file cursor, but they still need to store the fcntl file description flags, so yes. This is emulated by the Redox kernel for old schemes, by inserting fcntl calls between the legacy read/write calls that don't allow passing the offset and flags. However, I'd argue that the fcntl flags are even more client-oriented than the cursor, say, O_NONBLOCK. Should it really be possible for isolated processes to set each others' nonblock flag (unless using preadv2/pwritev2 which is non-POSIX)?
