Can a 220V AC to 12V DC adapter be plugged into 120V mains?
It would not be a good idea to try to plug it into 120V.  

Internally, that adapter is likely to have one of 2 options.  

Option 1: A simple transformer/rectifier/capaitor arrangement.
In this case, since the transformer windings ratio is fixed, you should expect to get about 6.5V out (12/220*120).
Although supplying a low voltage to your motor isn't likely to do much (if any) damage, it certainly won't perform as you'd like it to.
It will probably also be much easier to stall - which could lead to some damage to the motor and/or adapter.

Option 2: A switch-mode power supply.
In this case, the incoming mains AC is rectified &amp; smoothed to high(ish)-voltage DC and this DC is then 'switched' through a much smaller transformer at a much higher frequency than the 50/60Hz mains (typically many 10s of kHz).
These circuits can be designed to operate from a very wide range of input voltages, but this is not always the case as it would likely increase the cost &amp; complexity of the circuit.
If your adapter was designed for a wide input range if would probably be marked as such.  

The fact that your adapter's specs include a 'VA' rating lead me to strongly suspect that its an 'Option 1', since transformers are rated in VA.  

You should be able to source a suitable replacement locally. The specs you should be most concerned with are the output voltage (12V) and current (no less than 850mA - more is ok).