If you write to a file while someone else is reading it, then it can cause a problem - especially if it's a dynamic file. If it's static, you likely won't have too much of an issue.
However, just like if you update Internet Explorer, Firefox or any other program, they recommend to shut down the program BEFORE upgrading. This ensures that there's no corruption in the process. If your boss can't give you a few minutes to update a file, then there's something wrong in that picture too.
Application should already be tested and working, just need to shut down briefly, overwrite the file, then re-enable. If it's only one file, total time is less than 30 seconds.