Yes. Since the tube is firmly affixed within a handbreadth of the door, the air and the wooden base do not constitute an interruption between the scroll and the door.
 Agur B’ohalecha, citing Da’as Kedoshim Y.D. 289:4 and R. Shmuel Wosner in Kovetz Mi-Beit Levi 2:23. Cf. Minchas Yitzchak 10:95. The gap between the mezuzah and wall must be less than a tefach.