The 3 pin charger used with the classic series has 2 outputs, a constant current output for charging the NiCd battery and a constant voltage output to run the calculator. When you plug this charger into a 35,45,55,70 or 80, the battery is electrically disconnected from the rest of the calculator. The calculator logic is run from the constant voltage output of the charger and this does not depend on having a good battery fitted. It is safe to run those models from the charger without having a good (or any) battery installed.
The 65 and 67 as similar except for one important difference. The card reader sense amplifier/motor driver IC is connected directly to the battery back. So in those models, the votlage across this IC when the charger is connected is determined by the battery pack acting as a shunt regualtor. If there is no battery, or a defective battery, fitted, then that voltage will be much higher than normal. The HP65 manual acutally warns that this can do damage. The HP67 card reader IC was redesigned, hopefully to prevent such damage, but I certainly don't risk it!
The later models with 2-pin charagers all use the battery as a shunt regulator to limit the voltage. In the case of the non-contiuous-memory models, there is no danger in trying to charge the battery in the calculator with the calculator turned off (the logic is then entirely disconnected from the battery by the on/off switch). Turning such a non-continuous-memory model on while connected to the charger without a good battery is unlikely to do any damage, the calcualtor draws enough current to reduce the voltage at the output of the charger circuit to a safe level. However the calculator will not work correctly.
The continuous memory models (19C, 25C, 29C, 33C, 34C, 38C at least) use the battery to power the RAM chip even when the machine is turned off. This is how the memory is maintained. If you connect such a machine to the charger without a good battery fitted, a higher-than-normal votlage is applied across the RAM chip -- the RAM chip on its own does not draw enough current to pull the voltage down. This is very likely to do damage. With the machine turned on, it shouldn't do any damage to connect the charger without a good battery, but the machine can't work correctly. I don't risk it.
The Topcat (91, 92, 97) machines have a circuit in them designed to apply a load to the charger to keep the voltage down if it rises too high (that is, if the battery is defective or missing). As with the non-continuous-memory models above, it should be safe to connect the charger without a good battery fitted, but the machine won't work correctly. Now, this circuit only works with the machine turned on, and the (very rare) 95C uses the battery to maintain the continuous memory as you might expect. In the case of the 95C, therefore, connecting the charger without a good battery installed may well do damage (and on a machine where spares are next-to-impossible to find).
So to sum up, connecting a charger to a machine without a good battery :
35, 45, 55, 70, 80 -- Works fine
65, 67 -- May damage the card reader sense amplifier IC
Non-continous-memory Woodstocks, Spices, etc -- Won't work, may do damage, but it's unlikely
Continuous memory Woodstocks, Spices, etc -- Is very likely to damage ICs
Non-continuous-memory Topcats -- Won't work, but there is a protection circuit that should prevent damage
95C -- Is very likely to damage ICs.