I'm not sure which driver handle(s) you are inquiring about or what environment you are using it in. I'm assuming it's for 4mm precision bits, as that is the size that 000 size bits come in.
The 64 bit driver kit handle https://www.ifixit.com/Store/Tools/64-Bi... or https://www.ifixit.com/Store/Tools/64-Bi... for just the handle is ESD safe.
The handle is aluminum, a conductor, and it is not static generating. If you are taking very basic ESD measures (you are grounded to your work with an anti-static wrist strap) then it is very ESD safe. If you are not taking basic ESD measures like grounding yourself to the work environment and device you are working on with a wrist strap "ESD Safe" doesn't matter, any movement you make or tool or item you touch could potentially conduct through you and the driver handle to damage a circuit.
Non-metalic handled tools are different. Some info from the ESD association:
"If you ground a conductor (the conductive metal blade of a screwdriver for example) while it is in the presence of any item carrying electrostatic field (a charged piece of plastic, or clothing) the conductor will acquire an electrostatic charge that may be sufficient to cause damage when discharged. If the handle of that hand tool is sufficiently insulative, and if it does acquire a charge, it will remain on the conductive portion of the tool until it is brought in contact with a ground path, even if the user is wearing a wrist strap. That ground path might be an ESD sensitive component. In this case damage may occur both from initial contact with the charged hand tool and again when the charged component is grounded."