The value of a question in Parliament is its embarrassment value. Generally questions about specific individual cases are not answered on the Floor of the House, because no minister would have information on every single individual case being handled by his department. Typically, a minister would respond by either offering to look into the case or offering to discuss the case with the MP in private.
It can however go the other way. If the MP raises the issue and the Home Secretary wants to make an example of how tough/firm he is on immigration/overstayers, he can highlight the case in his own response and promise to take tougher action in cases like yours.
So, in short, a double-edged sword.