Thanks. I'm getting lots of good information about this situation, but so far nobody has addressed the specific question I'm asking. (Well, maybe MarkB has and it was too technical for me to recognize that he had answered it---I'm working on that.)
The question is, could it hurt the speakers to play them when the MP3 player is plugged in in its recharging mode, taking into consideration that the speakers don't recharge through the MP3 player? They recharge by being plugged into a powered USB outlet, which the MP3 player does not have.