Motors don't work that way. The speed of the motor is based on the number of poles in the windings and the frequency of the input current. The motor is going to try to achieve the same speed and same output power as long as the frequency remains the same. That means if the voltage drops the current is going to go up but the same amount of work will be done, but at the expense of more heat in the motor windings which over time may damage the windings.
Too severe of a drop in voltage will mean more slip and less torque in the motor output shaft and even more rise in current likely causing catastrophic failure in windings if overload protection does not open the circuit.
Now if you supply the motor with higher than nameplate voltage you have the opposite to some degree. It is still going to try to run at the base speed according to input frequency, but with a high input voltage the current is going to be lower at the same output level. But you can not raise voltage too high or you will go to and beyond saturation of the magnetic coils and will start to have increased heating effects from that.
So the basic answer to your question is yes the motor will run on 208 volts. It will draw more current when doing the same work than it draws at 220 volts. The real question is can the motor insulation take the increased heating it will encounter in the application?
That is something most of us can not give you a definite answer for, but in most cases it will work, may have a shortened life but end of life is probably years away and not hours.