Umm, no.
So, the question is...Does a person give a fuck if there are no fucks to be given at the moment? Do they give a fuck to patiently wait for those fucks? If so then that would mean they have a fuck to give.
*ponders this while drinking a cold Mike's Hard Strawberry Lemonade*
If one has no fucks to give, then they are in that sought-after state of blissful equilibrium. They are neither here nor there. Not even anywhere. They reside contentedly in a box and with a fox, shrugging off daily cares and drama. So no fucks are needed or desired. *uses a long straw to take a tiny sip of lemonade*