My company been doing this for years. My company administers the survey via a 3rd party who anonymizes the data (in fact there's no way to trace the responses back to you). Once the survey is taken, it's primarily 1-5 gradings, the gradings are made available to everybody, while written responses are not. You don't even have to write a response, you can just do the 1-5 gradings. Written responses are only used to clarify an issue - don't treat it as an opportunity to gripe and complain, you're being constructive!
All the teams then get a summary of their results and go over them and decide what would be best for them to focus on in the upcoming year.
The big thing for us has been discussing what the 1-5 mean, especially the 4 or 5. A lot of people are hesitant to grade something at a 5 because they can think of ways to make that better - but you should already be in an environment of continual improvement so you know you can always make something better. Therefore for us a 5 means it's going well and there isn't anything to address that the normal continual improvement process wouldn't address. A 4 then means mostly well, but it's not quite where it should be, a 3 means its well enough, and a 2 or under means here's an opportunity to improve things that will have a big impact on our processes.
It's all about identifying your sore spots and where to expend your effort at getting better.