I also own and enjoy an Isabella preamp. When you are in battery mode the power supply is essentially "off" since it is disconnected from the preamp and is doing nothing even though it is still plugged in. When you switch back to AC mode it comes back on line and will be charging the battery while you listen. When you turn your preamp off the charger will slowly bring the battery up to full and maintain it with a trickle charge. I can't see any value in disconnecting it - that will make no difference in the sound and, if you forget to plug it back in, the battery will go dead. Also, it will be hard on the connector on the back to pull that tight fitting plug out unnecessarily. Vinnie may have different advice but I think this is correct.
