I have white doves, and they do come back if they get out for about the first three days, but after that they leave, there have been multiple times of them getting out, and I was able to put them back after their return
The "white doves" you refer to are actually NOT doves. They are mislabeled white homing pigeons. This mislabeling is done for wedding releases where the uneducated feel having pigeons at their wedding is gross but doves are "romantic" and all. But labeling these birds as "white doves" when selling is sad on the sellers part (if they are educated).
White pigeons will come back. Doves are a different species.. the ones in the pet trade are so domesticated they have forgotten most of their natural survival skills.. and if you let them out they will aimlessly fly away and get killed by predators or starve to death.
Get while pigeons.. they are often called 'doves' which is confusing... but you can see they are bigger and the same shape as normal pigeons. You can also get ones with fancy fan shaped tails which look beautiful. These birds can be allowed out to free fly and they will return to their loft / coop if you train them.
Just sharing I found a young morning dove injured I cured him for a month, he comes every single day!! even knocks at the window when hungry now has a girl and both come to visit also he is not afraid of my dog because the month inside with us they socialized. Every thing is possible from this smarts birds.