If you are talking about a pickup like a 4-wire humbucker, assuming the other wires are connected correctly then yes the pickup would still work without connecting the ground wire. You would not get hum because the humbucker coils would still cancel it.
Grounding the shield primarily helps to reduce other noise from electrostatic sources such as flourecent lights lamp dimmers and the like. This noise can be clicky crackly or hissy sounding and many times can be more annoying than hum depending on the environment.