Manufacturers all instruct that their screw gate carabiners be used in the upright position when attached to your harness, but in many cases it doesn't really matter as long as it's locked and there aren't any burrs in either end of the biner that could abraid the rope, and your ropes are properly managed. But in general, its always better to orient them up as recommended by the manufacturer, especially if using a device that requires you to feed the rope through the biner.
Often lockers used in anchors will get burrs from metal on metal contact, usually in the end of the axis below the hinge, which can easily shred a rope. It's for this reason also that quickdraws have a rope and an anchor end, it can be disastrous if you swap them back and forth.
Situations where orientation would matter more than others would depend on what type of descender and biner you're using. If you were descending with an ATC and a pear-shaped biner, then you should orient it up so the rope is rubbing on the nice round profile of the ofset. If you're using a figure 8 and a D-shaped carabiner, then it ultimately wouldn't make a difference.
Orienting the screw gate down is a popular "gym technique". Gym techniques are typically implemented in an attempt to eliminate human error and avoid common mishaps, particularly by new or inexperienced climbers, but they are rarely considered proper use by manufacturers or experts.
It's a known flaw of screwgate carabiners that they can come unlocked because of rubbing, or vibrations, which is why many climbers will use pairs oriented with their gates opposite and opposing, but this flaw is also why so many other alternatives to screw gates are available:
(My personal favourite)
There are even screwgate biners with devices that will prevent crossloading which also work to prevent the screwgate from opening unintentionally:
Regardless of your biner orientation, if you find yourself in a situation where your rope or another rope is rubbing on your screw gate, you should stop dscending and manage your ropes before you procede. An upside-down screwgate can just as well be opened by a rubbing rope, though maybe not as easily.