Is this Possible

Doesn't much look like it:

http://www.nzembassy.com/thailand

http://www.nzembassy.com/thailand/new-zealanders-overseas/new-zealand-documents

Passports and Emergency Travel Documents

Only the Department of Internal Affairs passport offices in London, Sydney or New Zealand can issue a passport. A new online passport renewal service is now available. Please check the following link www.passports.govt.nz for eligibility, timeframes and frequently asked questions. In an emergency, most but not all New Zealand Embassies may be able to issue an Emergency Travel Document. Where postal sevices are irregular, the Embassy can assist with forwarding passport applications to Wellington. There is a separate fee for this service payable in local currency. Please contact the Embassy for further information.

Sure they can. Both my daughters got theirs from BKK.

The application will be sent to Wellington for processing but the passport can be collected, usually within about 10 days of submission.

IF the child is born in Thailand then you'll first need to process a citizenship via descent application before the passport can be applied for. So add another 2 weeks if your child doesn't already have proof of NZ citizenship.