Does publishing gives you an edge when applying for jobs in industry?
This depends upon your specific position within any given company. Check out Science Careers for discussions about this, but a summary of some examples for publishing and not publishing:


Some position will not require or expect any publications. These can be technical (e.g., run a machine all day or develop new proprietary methods), managerial, or other types such as sales. 
Some positions will want prior publications to show that you can complete research projects but not expect you to publish when you are working them.
Some companies such as environmental consulting firms expect their scientists to publish so that they continue to be experts in their field and highlight their publications on their webpages (e.g., WEST).
Some companies publish with their clients (e.g., look at the author affiliations on this publication).


In summary, publication expectations in industry range from none to regular publications. I suggest you find people doing jobs you are interested in doing, get to know them, and see what their specific expectations are for publishing. The Ask-the-headhunter blog contains suggestions for breaking into new fields as does the previously mentioned Science Career page. Also, the Chronicle of Higher Education has many resource for people seeking "alternative" careers (e.g., here).