Jim,
The "short answer" to your question is "yes", damage could occur if you "plug anything in, even if the gadget is rated for dual voltage".
First to clarify the terms. A Plug Adaptor is a simple and inexpensive mechanical device that allows North American plugs to connect to European outlets (and vice versa).
A Voltage Converter is a device which "steps down" voltage from 220 VAC to 115 VAC, to power devices which are only designed for 115 VAC (there are devices designed to "step up" voltage also). It's important to note that there are two different methods used for voltage conversion - Transformer or solid-state. Therein lies the potential for problems.
Electronic devices (especially those which use "switching power supply" technology) can be damaged if connected to a solid-state Voltage Converter. Most manufacturers recommend using only Transformer Voltage Converters with electronic products such as Camera or Cell phone Chargers.
The Converter would not act as a "pass-thru" but would deliver only 115 VAC and any devices connected would operate at that voltage, regardless of whether they were designed for "world operation". However, if the Converter was a solid-state model, the output voltage would be very "noisy" and not as stable as the sine wave produced by a Transformer (although a Transformer can't convert the frequency from 50 Hz to 60 Hz this isn't usually a problem).
If you're going to be travelling with both electronics and heating appliances, you might consider This Converter which combines both conversion methods in a single unit, with automatic selection between methods.
If you could provide more information on the devices you'll be travelling with, it would be easier to offer more specific advice.
Cheers!