If you try to pick block a mob spawner, it will not work. You can't control+pick to get data from them, either. However, you can use /give to obtain spawners (with data).

Steps to reproduce:
1: Create a new creative world
2: Type /setblock ~ ~-1 ~ mob_spawner
3: Look at the spawner and press the pick block key
4: it will not work.
5: type /give @p mob_spawner
6: It will work.