A roadster that is plugged in, is not really "off". It will provide power for heating or cooling of the battery pack if the temps get too high or too cold. This would be much more than a small idle load.
It will be interesting to see if Tesla will do the right thing and replace the battery packs at a reasonable price or create a PR disaster and then have to replace the packs anyway. So far HN and theunderstatement.com have the scoop. A search of the San Jose Mercury News doesn't show it yet. But there was mention of Tesla doing powertrains for Mercedes.