My husband's company does these annually, and part of the bosses' performance reviews include the "engagement" scores of their people. Great in theory.
First year, merely issuing the survey improved morale. Employees were so happy to be asked how they were doing, and to have an opportunity to directly and anonymously tell Management about various roadblocks to doing their jobs well (e.g., I need a new tool, this part of the process is really inefficient, etc.).
Year 2: engagement scores went down. WTF? Because the company didn't actually do anything to fix the identified problems, nor did it explain to the employees why it couldn't do X or Y or Z. So by year 2, the employees had written off the survey as more cynical faux-"engagement" consultant bullshit -- just one more Management "initiative" that takes their time away from their regular job and means nothing. Not only did they realize Management didn't actually care enough to fix anything, but they got to feel stupid for believing Management actually meant to do anything in the first place.* And let me tell you, nothing lowers morale more than getting someone's hopes up and then dashing them.
My favorite part was that my DH got dinged in his review -- he was one of those mid-level managers whose group morale went down. WTF? Almost every category was good! The employees praised him for his openness and interest in their career development and all of that! Alas, his score in the "I have the equipment I need" area was low -- the one area he had zero ability to control or fix. Awesome!
Tl;dr: Morale depends on follow-through. If you don't already have Management buy-in to fix the problems people identify and to be very open about how those fixes are prioritized, your survey will do more harm than good.
*The irony is that Management actually did mean to take action in response to the survey, but it had not developed a process to do so. As a result, they were overwhelmed by the number of suggestions and so defaulted to the easy/cheap options, like "let's throw a pizza party, yay rah go team!" and avoided the harder/costlier changes that actually might have improved people's daily lives. So lesson 2 is if you do intend to address suggestions that are made, have a process in place and responsible people identified to do so. And make the whole damn thing transparent! People will understand if you can explain that the budget doesn't allow you to do XYZ.