Yes but not very well.
The quality of depth generation output from stereo pair images is pretty tightly linked to sensor size and lens distortion. Camera arrays like this tend to use many low res cameras with wide angle lenses so, again, they are kinda bad for depth generation.
I found a blog full of tools for photogrammetry & depth map creation a while back that are great for getting a better handle on these limitations if you are interested:
You want LIDAR for making the point clouds, and a camera for colorizing them. Pure photogrammetry is doable (I think that's what Earthmine did for a while?), but it isn't as pretty or accurate.
For single-point-of-view, yes. Otherwise, if you can take images from multiple viewpoints, there are a bunch of solutions for pure photogrammetry, eg. Pix4d, Photoscan, Capturing Reality.
Theoretically, there is enough data in the images to build photorealistic models. Algorithmically, we aren't quite there yet.
Considering you can extract a point cloud from regular footage with parallax in it, even from stills, I see why not. It wouldn't be very accurate though.
I suppose you could use infared, similar to how the Xbox Kinect works. However, it'd only be good for indoor use and not as accurate.
I read that Tesla is experimenting with using radar and software enhancements to create an accurate point cloud. (To avoid the necessity of LIDAR)
If you needed it for something real and versatile (industry/production), you're best bet is LIDAR.
I haven't looked at the code for this FB camera, but I'd imagine you'd almost have to rebuild it as stitching images is much different? Seems like you wouldn't have to be as accurate with overlap on the point cloud.
I found a blog full of tools for photogrammetry & depth map creation a while back that are great for getting a better handle on these limitations if you are interested:
http://3dstereophoto.blogspot.com/p/software.html?m=1