Is there any meaningful difference between the terms undertone and overtone with regard to an utterance in the sense of an implicit meaning?
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As per dictionary.com
So it would seem that undertone is more about the vocal implicit meaning of saying something and overtone is about the way something is phrased.
edited to clarify which meanings I was referring to
An undertone typically refers to an implicit meaning conveyed by the manner of the utterance, that is, a literal sound in the voice that conveys the meaning. So words that are growled, hissed, or said "with an edge in the voice" carry an undertone such as anger, frustration, or sarcasm.
An overtone typically refers to an implicit meaning detected by "reading between the lines". For example, describing the consequences of certain actions in a perfectly neutral tone could still convey a threatening overtone.
So, undertone is conveyed literally by the sound of the words, while overtone is conveyed figuratively by the words themselves.
I like John Satta's answer for overtone, but take issue with undertone.
It can mean a low pitch sound in vocal conversation, but usually it means an undercurrent. Similar to overtone, but more subversive, or hidden; more a hidden feeling from the conversation. As opposed to overtone, which is the general implication of the conversation.