I have to disagree with The Evil Greebo.
The fact is that first off, metal edged corner bead is rarely used by professionals. When it is used, it's most often due to imperfections with the drywall (e.g. straighten out a not-quite-straight corner).
I can't tell from that photo if that's an inside or outside corner. If it's an inside corner then the metal should have been covered. If it's an outside corner (as I suspect), it can be very difficult to cover it with mud.
As I said, it's rare to see these. One area where it's more likely though is with regards to ceilings, and particularly soffits - areas where uniformity of various drywall sheets is more likely to be an issue. If this happens to you, I wouldn't sweat it.
As long as your edges are sanded well, use a good quality primer and paint, and it won't matter. You will not notice the difference. If in the future something gets damaged, the end result will be the same. A very thin layer of mud is not going to protect anything.
Caveat: I've installed paper, plastic, metal, nailed/glued/pressed corner bead. They all have their uses, pros & cons. Put it this way: there is a reason for all that variety in the drywall aisle at Home Depot. :D