Could writing a survey of the state-of-the-art in my field compensate for my lack of publications?
(I don't know anything about business school, nor much about academia outside of the US)

Three reactions:


Professors never have enough time. I seriously doubt they would be eager to read a long, unsolicited report from someone they don't know.
Further, a "review" type publication is not really research experience --  understanding a concept is different than being able to come up with and test new ideas.
On the other hand, if you do know what you're doing, a "review" of a certain field can be a nice service to the community. You could write it and submit it to a journal/conference or just post it on the arXiv. Then you would have a publication that you can list (depending on your timeline). 


Assuming the goal is to get admitted, the best thing to do would be to get some research experience by working for a professor. If that's impossible, and if you really are qualified to do so, writing a "review" for publication couldn't hurt -- though it's a lot of work and will likely have only a little impact.