Gen 2 power supply

Thank you. Is the adapter from the controller outdoor rated? My outdoor GFI has a plastic enclosure like the one below. I was wondering if the adapter would fit in the weatherproof enclosure.

Or is it better to connect a power cord to the outlet in the enclosure like the version from InSinkErator? Thanks.
http://shop.insinkerator.com/p/insinkerator-power-cord-kit