Not in the CPU, it's a separate component on the motherboard.
Lining the case will not help if it is the cable to your monitor that is leaking the RF. So you would have to wrap the foil around that cable, and earth it.
Or you could put another, very noisy, RF setup in the same room.
I don't think it has been shown that monitor cables are able to leak this kind of information as described in the OP. I also don't think it would be all that difficult to line your monitor cables (and mouse/keyboard cables if you want to get similarly paranoid) to protect yourself against this kind of attack