Yes by changing contact form 7 capabilities.
By default Contact form7 uses native wordpress capabilities. You can easily change this by adding a code snippet to your theme functions file.
Once you have added the new capabilities to you theme’s functions file, then use a capability plugin like for instance User Role Editor OR Advanced Access Manager, and add the new contact7 capabilities to admin user role as well as to editor user role. Your editor will then be able to view and export database entries.
Here is a link explaining what to do in detail: https://contactform7.com/2012/06/02/contact-form-7-32/