You don't have to switch to 12/12 for autos. They will flower regardless of what light cycle they are on, and many suggest that autos be left on an 18/6 light schedule throughout the entire grow, or 24/0 for veg and 18/6 for flower. Autos will not go back in to veg, but you will not maximize your yield if you switch them to 12/12 at all.
However, the other way would not work. If you have a photoperiod plant in flower under 12/12 do not change it back to 18/6 or 24/0 as it can either switch back to veg or Hermie on you