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Sort of. The stream is backed by a "real" operating system file descriptor, and when the process terminates the OS will clean up any open file descriptors.
Anyway, it's good practice to always close your resources when you're done, so close the streams :)
If you don't close streams, you may have problems opening them back up again. This is especially true if they're hanging off the end of sockets.
Closing a stream also makes sure that data is flushed through the stream if there is any data left to send.