Games : Does the Larder Door work with the Two Weapon Style talent?

The Larder Door is a pretty rad shield; it has solid stats, and more importantly, grants Bash, which allows it to be used as a weapon:

(Note that there is a second weapon displayed on the side there - Eder currently has a Flail and the Larder Door equipped.)

What's not clear to me however, is how this interacts with the Two Weapon Style talent. (Or, for that matter the Weapon And Shield Talent).

Does it?