We adopted both our fids from a rescue at the same time.
Our amazon had been in the rescue for a year and our Brown head for a few months.
The total time it took 3 weeks, but that was because it took us 2 weeks to decide and put in the application.
It was loud at the rescue, there was well over a hundred parrots there and some were pluckers. Ours didn't pick up these habits at all.
The adjusted really quick to being home with us, the brown head stepped up and started talking and whistling the first night, the amazon was beak grinding within an hour and came out of his cage that evening as well. They both seemed really happy to be in a home.
We were extremely pleases with the experience and if working with a good rescue I would say go for it. The rescue we worked with delivered the birds to our home and had a policy in place that we could return them for any reason within 30 days with adoptions fees returned. They came with their cages, toys and dry food to last a few months as well as some organic nuts.
The also let us call them anytime for support and information, they are really wondrful. I stay in touch and send them updates and pictures. One day I hope to have the time to also volunteer for them.