I would be concerned about the glue, since MDF is wood particles (i.e. floor sweepings and garbage), mixed with various chemicals and glue, and then press formed into different shapes. Rats will definitely chew the MDF, so they'd be getting some of the glue and chemicals in their system. Once they pee on it, it would be nasty and impossible to clean. Also found this little tidbit:
MDF (Medium Density Fibreboard) is made from waste wood fibres which are glued under heat and pressure. It is very versatile, but can be dangerous to use if proper safefy precautions are not adhered to. Most MDF slowly releases urea formaldehyde which is an irritant to the eyes and lungs. This can be sealed in with proper preparation and painting. The dust produced when sanding or cutting is another matter, and masks and goggles should ALWAYS be used when machining or cutting this material, and adequate ventilation should be present in the work area.
I think given the above, I would not use MDF for any part of a rattie house.