Sure. I believe it's called "Voxel" modeling. You set up a XYZ grid spacing unit and one XYZ unit is a Voxel. You then add/remove material Voxel by Voxel. Engineering based unit tolerances would probably make your Voxel size like about a tenth or hundredth of a milimeter 1/64-1/128th of an inch. May be a bit difficult to apply parametrics to a voxel based model. I believe @dcstaples is very familiar with Voxel modeling...
I don't believe so. I believe this is pretty much used in industries where preciseness is not needed. Most Mechanical CAD systems are based on NURBS modeling.
This biggest industrial use of Voxel modeling that I have come across to-date is for 3D printing. Of course, the 3D prints are "toys." http://voxelbuilder.com/
One up-and-comer is Monolith. http://www.monolith.zone/
My crystal ball says technology is going to move towards voxel-like modeling. Not in a geometric sense, but in a structural sense. Build atoms, to molecules, to custom materials, to generate shapes, to final forms, to 3D printing. As technology stands today, I'd much rather take a scanned image and convert it to voxels rather than facets. (Hmm, time for a google search.)
Designing the outside shape of an item and calling out a raw material isn't the future. Generating designs and materials from the inside out is. Next step, the Materializer(tm)*. Kind of like Star Trek Replicator, but real.
*Trademark still pending, but I'm totally going to do it.
Siemens should purchase Voxelizer.
There is also an interesting read by Interactive 3D Graphics. http://cvc.cs.stonybrook.edu/Publications/1986/KS86/file.pdf