At least for the power draw when idle, if it does, then it's either dumping the power as heat or self-destructing. You can't overcharge a lithium battery or you get metallic lithium in the cell and ruin and make it unsafe. It's certainly not going to be on the same order of magnitude as charging it for use. You'd need to actively design it to perform that badly, or have a dumb converter attached to the mains, to get a significant power consumption when idle if you had the neccessary circuitry to keep the batteries from catching fire.
As for the life of the batteries, that does depend on how they've done things. Some companies (panasonic's toughbook division) seem to rate their batteries at the capacity they'll have in the middle of their lifespan, which would pretty much leave the average MPG unaffected. But it'd be a nice question to have answered.