No, if you run out of conventional mines, you don't have an NSM. They way SFC makes it work, is that for one mine on an old Romulan Ship, using SHIFT-M will turn that mine into the NSM. Not sure how it works in a Multiplayer game, but you will be able to tell the difference by the color of the pulsing rings. A NSM has blue pulsing rings. Your opponents won't be able to see it (to them the rings will be red), whether your allies can see it or not is not something I am aware of.