I would say no.
This is a good idea. We do need some way to revise puzzles before they are released as the quality of puzzles has deteriorated in the past weeks. The "First Posts" review queue is not enough, as many new users post multiple riddles with negative feedback without changing their style.
There is are some problems though. Problems that are important enough to make the sandbox nearly useless.
How can we give feedback without knowing the answer?
The sandbox should be a place for the community to suggest edits for a question and make it better before it is actually asked, but without the answer, we cannot give feedback reliably. The reason this works over on PPCG is because there is no right answer. The OP there does not have to provide the correct answer, simply because the question doesn't depend on the answer. He might post a basic, ungolfed solution alongside his question just to show the answerers what to do, but the community doesn't need the best solution just to give feedback.
I don't see how this would work with Puzzling, however. I have seen many puzzles that seem unsolvable at first glance, but when I read the solution, it was just a well-crafted puzzle. I think the majority of the time, users would not be able to help improve the question effectively if they don't know the difficulty of the question - after all, if the puzzle is very well-crafted, then the solution may not be easy to find.
How can we ensure that the people who view the question in the sandbox don't have an advantage over others?
This results from the fact that there should be a single, distinct solution to each and every puzzle, assuming it is a challenge question. Using the PPCG example once again, a user may think they have a good solution. Once the question is released, they can post it whenever they want. Unless they happen to find the perfect solution somehow, there will probably be a better solution, whether it is one that is more creative, or one that is shorter.
Here on Puzzling, once someone finds the correct solution in the sandbox, they will try to post it as soon as they can when the question is officially asked. For some users who don't visit Puzzling Meta, they will not have those extra few days to work on the puzzle.
Again, I do feel like we need a way to revise most of the puzzles that come into the site. I just don't think a sandbox is the way to do it, unless we have a way to prevent these problems I mentioned.