An unencrypted, cryptographically secure hash, should in theory not provide any hints about the content of the message, as long as the message is unique. But when an eavesdropper suspects that the message is one of a finite number of known messages, they can compare the hash to the hashes of these known messages and find out that it's one of them.
Example: Let's pressume that I would have obtained an illegal copy of a copyrighted movie, and now I would want to redistribute it to you. The copyright owner is suspecting me of movie piracy, and is thus eavesdropping on our connection. They are aware of all the illegal copies circulating on the internet and obtained them themself to calculate their hashes.
When I use your encryption scheme, they could see the hashs of the files I send and compare them to the hashes of the files they have copies of. When they find out that one of my messages matches one of their hashes, they have proven with extremely high certainty that I distributed their copyrighted content even without having to crack the encryption.
Adding a salt doesn't help much, because when the salt is unencrypted, they can just recalculate the hashes of their files with the salt of each message.
Adding meaningless data to "muddy the water" before the hash isn't adding any security, because it's only security by obscurity. It won't take long for a cryptoanalyst to notice that the data can be ignored.
Conclusion: Better encrypt the hash together with the content.