Personally, I would pull the cover to catch the shavings because that's the sort of person I am.
However, if you presume the shavings will eventually settle in the bottom of the diff and hopefully won't be agitated during normal use then maybe they won't find their way into the mechanism, ruining your life forever and making you sterile.
It could depend on the size of the swarf as you cut. Smaller stuff might not be an issue. Larger stuff will sterilize you.
*Nods knowingly*