You cant totally play a song with your mind unless its a simple monophonic melody. So many instruments, effects etc its hard for the mind to reproduce exactly but sure it keeps the general idea (melody) of the song.
A born deaf can't hear a thing with his mind like a born blind can't reproduce or see any images/colors because his mind doesn't know how to do this
There are savants who can replay complicated piano pieces after only hearing them once. Their brains are wired funny but they can do it.
Some guitarists I know remember the chords of a song well enough to piece them out string by string on the guitar... so they are hearing more than the single not. I can do that for piano sometimes, too (and sometimes guitar) but then it's more of a "no, that chord still isn't right but let me try this instead" case). My brother once tried to show me how to piece a chord together on the guitar from memory but my brain doesn't remember the same amount of information his does.