Since the Stack Overflow Careers site is not included in the API, I doubt that you would be able to create an application using it. Since it is a revenue generator for Stack Overflow itself I also highly doubt that there will ever be a public API for it.
So in context of your question, you won't be able to charge for the application since the API for careers does not exist.
In general, there is no rule that says every Stack App has to be free, it is up to the developer to decide whether he believes he has an application which the community will actually spend money on, or if he or she wants to distribute it for free. However in the Stack Overflow culture it would most likely be better received if it was free or donation driven, since the Stack Overflow sites themselves and the content of the sites are free.