Locked is probably illegal, having said that I have been through a full inspection a few times ages ago with a locked diff in a vl and was passed each time.
Yeah, chanhung the diff oil is a good idea, but the fluid that does the work, the viscous fluid, is actually sealed inside the diff center. You can't get to it. The fluid that drains out is just lubrication for the bearings and gears, and has nothing to with the limited slip function of a viscous LSD.