I have seen and heard deer cough before, it is a very unmistakealbe sound, and yes it does sound just like a person coughing. It dosent sound anything like a grunt or a snort wheeze.
I was watching a doe waiting for a shot at her last year and her vitals were covered by a tree when I saw and heard her cough. I was just amazed by the fact it sounded just like human cough[]
I also watched and heard a small button buck cough this year.
Ya ought to hear the sound they make when they run into a tree at a full run[&:]

" GOLDEN KEY FUTURA STAFF SHOOTER "