Yes. Even if the room was a mere cubicle, and none of its walls reached the ceiling, it would be obligated with a berachah, if the wall is at least ten tefachim high and the door itself has a lintel. This is common in home offices.
 Mezuzot Beitecha 286:14:54; Shevet HaLevi 2:151; Agur B’ohalecha 25:15; Cf. Pitchei Mezuzot 286:14:87.