Theoretically this sounds right - so much so that others have done it. The problem is that none of them have reported regaining rankings. Possible issues I can see:
1. Once Google has identified bad backlinks they want the webmaster to go through "due diligence" on a clean-up.
2. By deleting a page you might sacrifice the target page for other links that were helping you, or you might be breaking the circulation of PR within your website.