Why does my shaded pole motor barely rotate when driven at 1/2 its rated voltage?
The RPM at constant torque is (more or less) proportional to voltage on a shaded pole motor with a fan load, which is why simple triac speed controls work fairly well (again, with a fan load only). 

(Image from this Masters Thesis. 



Figure B represents the fan load as a function of RPM

Figure C represents the transfer function of the motor-fan system at different voltages. 

As far as the motor characteristics with **non* fan loads go, here is what they look like (from Standard Handbook for Electrical Engineers, 8th Edition (1949))



The mass of the fan is not so significant, the friction is important. Starting torque on shaded pole motors is low, as Tony says, and as you can see from the above curves, it's less than 50% of maximum torque, a stark contrast to many motor designs which have a much higher starting torque than running torque.  

You should be able to test it. Since you're in the US you can get 240V fairly easily from a dryer outlet etc., sometimes even from multiple 120V outlets. 

If the motor shaft turns completely freely (if you spin it, it doesn't immediately come to a stop but at least turns a few times around) it's probably okay. If it binds, probably better to buy a new motor.