VpnDrgn has the idea. Great job by the way. We have the same 'helping hand' soldering setup. The one with the two alligator clips and magnifying glass? I like it.
If you have protected Li-Ion batteries, they have a temp vent that will vent the batteries to keep them from building up pressure and exploding in the event that they get too hot. If the vent blows, the batteries are toast but you're house most likely won't be. Now that circumstance comes about because of a battery failure and isn't something that should happen if everything is operating normally. You can see from VpnDrgn's diagram the basic idea I was describing and was hesitant to describe in more detail.
The idea here is that you are using the guts of a charger (the charging circuit I mentioned you could build) and plugged the battery into the charger using wiring. You can see that his DC jack jumps across the atomizer so there is no need to have the momentary switched pressed for the charger to charge the battery and means that the LED and atomizer that would be connected are also kept in an open circuit while the battery charger is plugged in. Now, if you press that button while the charger is plugged in, you have a problem. That could be a good reason you'd want to remove the battery from the device for charging.
"Do most chargers/battery protection circuits prevent this in case they are left on charge for longer than needed?"
Yes and no. Expensive chargers certainly can meter your batteries and know when they are charged. Even more expensive chargers (intelligent chargers) can be programed how to charge your batteries using anything from time to voltage readings from the batteries or just about anything you want. As your charger gets cheaper, understand that it will have less and less of these features. Very simple chargers simply supply current to the battery and have an LED that comes on when the batteries come somewhere withing the peak voltage output they are rated for, but still don't stop supplying current. This is why they say to take your batteries off the charger when the light comes on and not to leave them on there. Simply put, if you leave batteries on a charger too long and your charger keeps pumping current in them they are damage and their life is shortened.
Sorry if this made your idea complicated. Keep in mind that you're a modder! Grab your wallet and soldering gun, gird your loins, and keep your mods in your garage when they're charging so if they explode you don't loose your house! Good luck and I'll watch this thread if you have more questions. I'll do my best to answer them.