Can the motor itself be damaged from this movement?
Sideways movement or "end float"
(as indicated by C below) is unlikely to cause any damage to the motor.
My motors were all fitted with a wavy type of spring washer as standard to help reduce this particular type of movement.
Although it is usually possible to exert enough sideways force by hand to compress the spring washer and cause visible sideways movement of the hub, this is unlikely to happen on a conventional bike during normal use, but it may be more apparent on a non-leaning trike when cornering.
Excessive radial movement
(as indicated by A above) could eventually allow the magnets to rub against the stator when a heavy downwards force is applied to the axle and would result in a very obvious metallic vibrating sort of noise, but I think it would have to rub quite hard before the magnets would suffer from more than just surface scratches.
Alan