Hi, i'm planning to use arduino pro mini 3.3V on a climbing robot but i'm not sure if it will work because i'm only allow to use two AA batteries and a Motor 273-0223 motor.
The short version seems to be that it should work okay.
The motor you listed has a nominal voltage of 1.5v, so it should also run fine off the batteries. Presumably the person who assigned you the project knew this.