No, at least not on Linux it’s fine to close the file.
The manual page clearly states:
On the other hand, closing the file descriptor does not unmap the region.
For portability, I also checked the POSIX manual, it says the same thing (although even more clearly):
The mmap() function adds an extra reference to the file associated with the file descriptor fildes which is not removed by a subsequent close() on that file descriptor. This reference is removed when there are no more mappings to the file.