The monument being erected for the Unknown Citizen is probably similar to the Tomb of the Unknown Soldier and other monuments praising those who have fallen and died in the line of duty. It should be a tribute to those fallen who could not be identified by name.
However the speaker in this poem is being more sarcastic. Instead of truly being an unknown soldier because of a violent death in war, the citizen is unknown because of a lack of indivuality or importance in modern society. He is simply referred to as a number which is mentioned in the first two lines:
To JS/07/M/378/ This Marble Monument
Is Erected by the State
The speaker is an unnamed commentator who is trying to use veiled sarcasm to show the idea that people have lost their individuality and are now being lumped into a pile of conformity.
The Unknown Citizen is such a person. His monument is being erected to celebrate his life, his service to his community, his family, his responsible nature, and the like. His days are filled with the monotony of filing insurance papers, working and purchasing approptiate middle-class items.
The last line of the poem, however, suggests, the narrator's true them.
Was he free? Was he happy? The question is absurd:
Had anything been wrong, we should certainly have heard
Is this living "below the radar" idea, living as drones, truly what makes a person alive? Through the sarcasm, the reader understans the answer - NO.