I wouldn't think they need to be upright all the time. However, if you're using a top coil then keeping it vertical will prevent the liquid from seeping into the coil area. If it has a short wick it might require a couple of primer pulls (pulls without pressing the fire button) to keep from getting dry hits.
If you are using a bottom coil like the Kanger T3 then I've found horizontal is the best position. This position helps prevent gurgling but still keeps the wick moist for immediate
vaping.