The cabinet will probably have to have a filler strip for two reasons I can think of. One is the walls are probably not square with each other, and if the cabinet is pushed right up against the two walls, there may be a resulting gap between the side of the cabinet and its adjoining wall. The second is the drawers may be too close to the wall and could scrape against the wall as they are pulled out or pushed in.
The solution is usually to add a filler strip. This strip should exactly match the cabinets and will look good in the installation. I would think in this type of installation a strip of 1 to 2 inches max would do the job.
Good Luck!
Dodgeman