I'd doubt it. Decent chargers for yonks use a sensor in the battery to prevent this - or other methods. I can't see the purpose of providing an 'overheat' warning when it is just as easy to prevent it. But presumably you don't have the handbook to check?
Thing is what you're describing - an interruption to the power supply while charging - is quite common on a building site, the home of such pro tools. So I'd expect them to cater for it.