Audio-Technica ATW-T1802 and the Rode NTG-3
 

I am thinking about buying the Audio-Technica ATW-1823. Will the Rode NTG-3 work with the ATW-T1802 transmitter? Will it provide sufficient phantom power? Thanks!

As an owner of the AT 18XX series including the plugin transmitter I can tell you it does NOT provide enough phantom power to power that mic. You would need either a seperate phantom power supply or a different mic.

You will have to connect the mic to a Sound Devices MM1 to provide Phantom Power, then connect that to the transmitter. This has the advantage of allowing whoever is handling the mic to also monitor audio on headphones via the MM1.

You will also need to have an attenuator between the MM1 and the transmitter as the MM1 provides line output. The transmitter is expecting mic-level input. An Audio Technica AT8202 works well for this.