Is it possible to experience the mountains/desert as a day trip from Fez/Marrakech?
It is not possible to do a day trip to the desert from either Marrakech or Fes. Its about an 8-hour drive from Fes to Rissani, and just as much to Zagora from Marrakech.
You can however, reach the mountains from both within an hour or so. From Marrakech, try Kasbah Toubkal. The High Atlas are more spectacular than the mountains near Fes.