Yes it would.. Why would you do this? .. it could easily poison people. Nicotine can be FATAL.. dont believe me.. google it. They USE to sell nicotine liquid in pharmacies years ago in small dark colored glass bottles . but when people accidentally broke them and cleaned it up with bare hands and towels etc.. they DIED because nicotine went into their skin and poisoned them.
Ejuice is almost exactly what goes in a fog machine. So yes, it will make fog, though flavorings make poor scents so it won't smell pretty or anything. There's no reason to use actual ejuice rather than pure glycerin or propylene glycol.
You wouldn't use nicotine juice for this, of course, for the reason stated above. Besides the danger, you're also wasting a rather expensive drug, whereas without nicotine ejuice is damn cheap. So you'd be killing your friends and wasting money by filling a room with nicotine containing vapor.
Fog Machine Vape
Did this last night, but it was diluted. Don't worry, no one died...