I cannot say whether or not the New Zealand police will notify the uk authorities or DVLA. However regardless of this, there is no mutual recognition of disqualifications between England/Wales and New Zealand.
Whether or not you will need to disclose this information will depend on the question asked. If for example, an employer or insurer asked whether you had ever been convicted of a criminal offence, you could not say no. You could however explain that it was in a different country and so the law was different.