In my experiments doing just this, some seeds will be auto flowers, some will be normal photo period plants and some will be "fast/early" versions that flower like photo period plants, but a couple of weeks earlier and finishing within 6 weeks or so.
They seem to produce a (F1 generation) ratio result of roughly 25% autos, 50% photoperiod and 25% fast/early versions.
You will need to cross plants from the newly made auto flowers with themselves (F2 generation) to stabilize the auto flowering genes and to produce plants that breed true for the auto flowering feature.
Yes, some instability, but without experimenting, you will never know!
You will also have to grow quite a few F1 plants to identify your autos/photos/fast plants from each other, then select the best examples to breed your F2 seeds from.
Hope this helps, Organoman.