Yes. But traditionally Unix filesystems provided stronger consistency guarantees than required by POSIX, and applications have come to rely on them. Actually, in the event of a crash I think POSIX specifies implementation-defined behavior even for fsync.
Making fsync a no-op and not having any durability at all is perfectly POSIX compliant. POSIX only concerns itself with the visibility of I/O in the live system (e.g. a process either sees a write fully realized, or not at all - this didn't use to be true for larger writes until fairly recently, btw.). POSIX specifies nothing about what happens when a system is restarted or looses power.
