No. They do not prosecute people based on clicking the link. They merely obtain a search warrant. They will prosecute people if they found any CP based on the search warrant.
There is definitely problem with the methodology used by the FBI here, but the real problem is this law. I guess I understand the reason for laws against planning to murder someone... but planning to copy some bits to your computer that represent a naked kid?
Let's spend our money going after people that actually physically rape children, not people that click links, or that think about thinking about clicking links.