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.
You might also like to look at the problem as an excuse to buy tools with li-ion batteries, that don't mind partial charge and discharges.
I just bought this bundle from Bosch:
Headlights, all day, no I think not. Two headlights are (as you say) about 100 watts (to be exact they're probably 110 watts, but I won't quibble). If you left them on for 10 hours (a lot less than "all day") they'd take something like 8 amps for 10 hours which is 80 ampere hours which is more than the capacity of most car batteries so your battery would be fully discharged I'm afraid.
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