This question is pretty self-explanatory. Gas seems to only go down while driving manually or automatically, but since fast-traveling also relocates the Regalia, it only makes sense that Noctis and co. are driving the Regalia during this time. I haven't experimented enough with fast-traveling much as of yet, since playing other games while auto-piloting across the world to get lazy AP has been my strategy lately, so I'm not sure if it's possible to run out of gas while fast-traveling.
If this can happen, does the game tell you? Or is it just not possible?