What happens when you close the Unassigned Time Project?

We originally implemented Project Costing and Billing in a professional services environment. Then as a later phase we added Project Resource Management and Project Management. We have a key user complaining about the project that we added for Unassigned Time. This project is showing on their custom reports. The easiest way to get rid of this from the reports is to change the status to closed. Will the negatively impact the calculations for unassigned time?

Is the only alternative to exclude this type of project from all our reports?

thanks

Lizelle