Essentially, I'm wondering if an octet stream is, by its nature, secure without knowledge of a semantic meaning for the bytes being sent. If you have no knowledge of the processing at either end of the stream, is there any way to get information from it?
Real-life data has a lot of structure which makes recognition easy. The Unix
file utility has done so since 1973.
Not being able to figure out the ins and outs of a bunch of bytes means that the bytes are not distinguishable from random, unless you know a "secret convention" which governs the interpretation of said bytes -- this exists and is called encryption. Decades of research in cryptography have come to the following conclusion: encryption can exist, but it is not easy. If you do not apply encryption explicitly, then the meaning of the data is not secret but, at best, obscure. Experience shows that obscurity rarely lasts long.
This would be known as Security by Obscurity, and I wouldn't count that as security.
The ability to derive information from a given stream depends on the protocol or technology that created it, nothing more or less.
To keep information private, you'll need to use an encryption algorithm. Even with an algorithm applied to your stream, it could be insecure depending on where the stream is. Is the stream on disk, or is the stream on the network?
Often times if the encryption itself isn't broken, the key exchange is. Depending on the value of what you're protecting in the arbitrary stream of bytes, it may or may not be worth it for a black hat to decipher your stream.
Given enough time and motivation, any non-standard cryptography will be broken quickly.