Your comment #1 seemed pretty weird to me. How can the Dot speaker make a peep if a speaker wire is plugged into it? Doing this takes the Dot speaker out of commission, whether the speaker wire is unplugged at the other end, or is plugged in at the other end to a speaker that is off, or even if it is plugged into an orange. Nothing can make a sound this way.
Now, that's not saying you did not hear sound out of the Dot. This can happen if the audio plug is not plugged in all the way (even if you think it is). I have two Dots and one's jack is so tight, that it takes a good push in to get all three contacts of the jack to open and contact the plug, and this likely happened to you, too. Try this again, and this time be sure you have that jack in flush; all the way in with no metal of the plug exposed. If you get sound again, then I'd say the jack of the Dot is defective and not making good contact with the plug.
Again I will say, the Dot speaker will be silent if a plug is correctly inserted into Dot, whether the other end is left unplugged or plugged into a speaker.
What you described has never happened in my experience, and the Dot is plugged into our stereo AUX-in. We never need to listen to the Dot's speaker; since our amp is left on 24/7/365 because we are always using it for something since all our gear audio goes through this amp. We just select the source knob for whatever we want to hear. The TV's audio source was usually left on the amp's input, and two clicks away is the Dot audio, and now that we have a Dot, that is the source we are keeping the knob resting on nowadays.