I think "uh-huh" is simply an acknowledgement that the listener is simply listening. When a piece of hardware sends a piece of data, "packet", the receiving hardware acknowledges its receipt so that the next packet can be sent. if the acknowledgement is not received, the data packet is sent again. That's why your connection speed drops when you are further away from the source. Some packets which are lost, not received intact, or "dropped" have to be sent again, reducing the effective speed of communication.
I suppose it could be construed rude. I can't remember an instance when I thought it was rude to have my narration punctuated by unsolicited "uh-huh" .

What I am about to say is a bit OT, but related to this issue. Indians say what sounds like "hmm, hmm" or "hun" ( the "u" is short as in put, to place). It's the same as "uh-huh" . It's technical name is "hunkaar", comes from Sanskrit, which means the sound of "hun". It's a part of story telling, rather listening, etiquette. When you fell asleep, you stopped uttering it. That was a signal for your grand mother, aunt, mom, or dad to stop telling the story.