The implied access and license is probably valid as long as you're abiding the ToS. If you're violating the ToS after agreeing to it ("agreeing" means that proper notice is given to make the ToS binding, etc.), the implied license would probably not work. If you've been specifically asked to stop, either directly or indirectly (e.g., through an IP ban), any implied license or access privileges would almost definitely be revoked at that point.

>At least in Europe, news organizations pushed this kind of argument in their campaign against adblockers and failed in front of the courts. US law may differ, of course.

Ad blockers differ because they alter the payload after receiving it under legitimate terms (though this could still probably be considered copyright infringement under the argument that the license is for viewing only, not alteration). The CFAA would not be applicable because when the adblocker comes into play, you're not accessing someone's network (which is what the the CFAA addresses).

If a site clearly disallowed AdBlock users in their ToS and adequate notice was given to users that they were to be bound by these terms, it would be "unauthorized access" to the server, which is not allowed under the CFAA.