yes, including the hash has another advantage as well: the data can be mirrored somewhere else, so that when the original media server goes down, it can be retrieved from somewhere else and still be verified
this is great for logos, emojis and such, any data should have a virtually infinite lifetime
that said, that kind of mirroring shouldn't happen without the author's consent, and for more privacy-sensitive/temporary images it can be better to not include a hash, exactly to prevent this and even have a degree of plausible deniability