Most community shelters will spay/neuter an animal before it is placed for adoption.
Dogs will be evaluated for temperament and socialization as well as how they get along with kids and other dogs. Also housebreaking will be a determining factor.
The older the dog that is not house trained the more chance of problems in that area.
Her chances of being adopted are contingent on how crowded the shelter is, and how social she is, as well as how long they keep animals depending on the crowding factor.
The more adoptable animals will trump the less adoptable animals.
Every shelters protocol is different so you need to research the policies of the different shelters in your area.
My local county animal services keeps animals for a long time, they do their best to not have to euthanize, but, this is a sad fact of the over population issues with cats and dogs, especially this time of year at the peak of breeding season.
You can try running an ad on a site like craigslist and screen potential adoptees, maybe go to their home, see where the dog will be living, ask if they plan on making her an indoor/outdoor dog, if they can afford upkeep and health care.
If you choose to give her to a private party I would tell them that if it is not working out you would like to know so you can help place her again.
If you are asking for a guarantee that she will not be put to sleep by surrendering her to a shelter, well, there is no guarantee, this is why spaying and neutering is so important.
Good luck and I am sorry you have to let her go.