magnet pickup built under/into acoustic bridge?

[Greenfuz]

would this work? for some reason I feel like it wouldn't, but it seemed like a cool idea

[Paragon]

Not with a magnet pickup. They use the string movement through the magnetic field. Not much string movement right at the saddles. That and the distance from the strings would most likely be too much.

Standard acoustic pickups under the saddle are piezo pickups.