Current unbalance generally indicates a problem with the windings of the motor. Voltage unbalance usually indicates a problem from the feed of the motor, such as a transformer that is failing. The relationship can be related, but generally I have seen them as separate issues in an industrial environment (my knowledge and experience is limited however!)
The motor life can be affected greatly over time, if not ending the motor's life immediately, if the unbalance is large enough. Very small motors can be affected with small current unbalance, as large motors can tolerate small current unbalance. Even a 60hP motor will only tolerate a few amps (10A or so) imbalance w/o affecting its' lefe expectancy over time.
Efficiency will be affected by current and/or voltage unbalance as well. If an unbalance occurs, more heat (I2R) losses will be induced on one winding vs. another. These winding losses will create an induced field, which in turn will lower the efficiency of the motor. Motors are by nature inductive loads anyway, so the addition of an unbalanced circuit on an already inductive load will only create more losses.
I one time had an instance of a motor that burned up because of an old and dirty fuse clip. The fuse clip made it run partially single phase.
The people who ran this plant in the company had to call our plant and have me come over. The rewound motor did not get up to speed and was tripping the motor overload relays while idling.
I checked the connections for correctness and ran amp checks and voltage checks. There was excessive voltage drop in this one fuse block so I cleaned all of the fuse clips and blades and put the fuses back in using Ilsco Deox(R). This was a 90 year old plant so this was a good thing to try. The motor ran like champ.
I have become a believer in doing periodic voltage amd amp checks of all 3 phases. A motor is not going to tell you if it is slightly overloaded or if it is running partially single phase. The international style relays will not detect small amounts of single phase imbalance that will slow roast a motor - they are not precision instruments.