Can wood floors be refinished half a room at a time?
No.  You really can't.   

There are several reasons why:


Dust.  Sanding dust will get everywhere.  Ideally you want to move everything into one room, that will hopefully not be refinished, seal off the door and do everything at once.
Equipment Rental.  It is simply not cost effective to rent the sanders for multiple small periods of time.  If you try and do half a room at a time, you'll be paying many times the price over doing it once.
Finish Quality.  When painting anything, the general rule is to always maintain a wet edge.  That is, in the middle of an area, keep painting until you get to a wall or other natural boundary.  If you let the paint/stain/varnish/polyurethane dry in the middle of the floor, you'll end up with an unsightly ridge when you go back to finish the job.