Having multiple developers work on a single file is only a problem if you have no version control, or are making massive changes.
A well-written CGI::Application module would not have much in the main class. It would be calling other classes to do most of the work. The main class just translates web requests into method calls on other classes.
Any project large enough to have a team working on it will have multiple CGI::Application modules. I like to split things up into logical "applications" so that if Jane is working on the address book app and Jim is working on the calendar, those will be separate modules.
In practice, I've never had a problem with teams using any kind of MVC approach like CGI::Application.