Is Kiwi Codes Project Browser a full replacement to the "Out of the box Browser"?
Yes it is. It has all the functionality of the built in Revit browser plus a lot more functions.
Can you run Kiwi Codes Project Browser and the built in Project Browser at the same time?
Yes you can. You can also have some team members working in a workshared project without KC PB installed and some with it installed, both working together no problems. Obviously the added functions of KCPB will not show up in the builtin project browser ie custom folder structure in Schedules and Legends.