Train gamer, Euro gamer and War gamer
The Detailed Rules states it this way:
The effect of the prior when building
After having built a building, you can use your prior to immediately use the function of the building. Place your prior onto the newly-built building.
(You can only do this with your prior, and only if your prior is available.)
So getting technical, it says you may immediately use the function of the building (by placing your available Prior). This would imply also being able to take the action.