Speaking etymology here, folks.
So some online hacks will have you believe that 'yum yum' is a phrase indicative of baby-talk and first came into usage as an interjection in the later Victorian period. I'm having trouble believing that.
The American Heritage Dictionary (probably the best portable book on American usage) says 'yum' is onomatopoeia, presumably having to do with the sound induced by gastro-olfactory hypersensitivity. I think this more likely.
However, there is a third rail.
The Indo-European root 'yeu-' is the source of the Latin word 'iuventis' and the Germanic words also meaning 'youth' or 'vigor'. Now, I realize from an etymological point of view that it is highly unlikely, but wouldn't it be nice if the word 'yum' was a generations-removed derivation from the very ancient Indo-European word meaning 'possessing youthful vigor'.
Would that be the case, perhaps it would suggest that yummy food is indeed the source of the fountain of youth.