I think the game already does this, more or less.
No, it doesn't. Transparent bricks will occlude light flares and most emitters, but not bricks. Same for solid bricks.
This is actually a good idea, and I would very much like to see it ingame, but would be hell, both to script and to run, due to the fact that if you were to place, say, a 1x5x4 (wall brick 4 studs wide, 5 bricks tall), the client would have to stop rendering all the bricks behind the occlusion brick. Said brick would have a relayed script to calculate what the player's perspective sees as "behind the brick", using the player's position and rotation, as well as the brick's own. I'm not sure how this would work, due to brick datablocks being on an alignment grid, whereas player/bot/vehicle/weapon datablocks are not grid-aligned.
Something similar to zone bricks might work more efficiently in this case, making a check on what bricks are within the zone of occlusion (or outside of it). However, it will still have to constantly relay this script, causing a ton of client lag or desynchronization; this would most likely leave you at a worse framerate/resource usage than before.
Even with all the logic I've provided, I would actually still like to see this in some way that wouldn't be hard on the engine/resources.