Hypothetical:

You are a loyal American in a position political leverage

You are threatened with damning blackmail on you/spouse/kid by the DS (stick) & offer you power & money potential (carrot)

You suspect Q is real & contact them via the White House

What does the Q team do?

Possible Ans: They tell you to 'play along,' Use you as a double agent (if possible), gather evidence, trace back & expose any DS structure that is revealed. And they move to destroy the blackmail.

You probably end up out of public life, but as free from the grip of the DS.