Does everyone have to exit the Revit model for me to Export/Import parameters or families into Revit?

No, but we recommend that you make sure you are working in the latest version of the model.  Also if anyone has ownership of any doors, the Export process will generate an alert and give you the option to skip those doors or cancel the process. 

NOTE:  It is good practice to have other people working in the model save to central before beginning the Export process if you think they may have made changes to any doors.