I have heard that as long as the inside of their gills are still wet they should be fine... yes get some stress coat, and make sure you have a lid with AIR holes. their organ that allows them to breath out of water makes them need air, if they cant get to the surface for fresh air they can drown... yes your fish can drown from lack of oxygen.
keep us posted :) hope shes ok.
I have also read somewhere about somone finding a betta still alive in a trash can and the betta lived more than 5 years after that.