From what I remember of the schematics :
Classic models without a card reader (35, 45, 55, 70, 80) can be safely used on the adapter with no battery in place. When the adapter is plugged in, the battery is disconnected from the calculator.
Classic models with a card reader (65, 67) can damage the card reader sense amplifier chip if connected to the adapter with no battery fitted. This is particularly true of the 65 (the chip was re-designed in the 67).
Woodstock, spice and sting models without continuous memory should not be connected to an adapter with no battery in place. It is unlikely to cause damage, but I wouldn't risk it.
Woodstock, spice and sting models with continuous memory MUST NOT BE CONNECTED TO AN ADAPTER WITHOUT A BATTERY IN PLACE. Sorry for shouting, but this is the most common way to ruin the (HP custom) RAM chip and possibly other parts.
Topcat models without continuous memory (91, 92, 97, 97S) will not be damaged if connected to an adapter with no battery, but the printer and/or card reader may not work properly. There is a circuit built into these machines to limit the supply voltage under these conditions.
Topcat models with continuous memory (95C) must not be connected to the adapter without a battery in place. The same protection circuit as in the other topcats is there, but it only works with the power switch 'on'. There is a very real risk of damaging the always-powered RAM chip if connected to an adapter with the machine turned off.