(B) INTERNET SEARCH ENGINES- A provider of an Internet search engine shall take technically feasible and reasonable measures, as expeditiously as possible, but in any case within 5 days after being served with a copy of the order, or within such time as the court may order, designed to prevent the foreign infringing site that is subject to the order, or a portion of such site specified in the order, from being served as a direct hypertext link.

(D) INTERNET ADVERTISING SERVICES-
(i) REQUIRED ACTIONS- An Internet advertising service that contracts to provide advertising to or for the foreign infringing site, or portion thereof, that is subject to the order, or that knowingly serves advertising to or for such site or such portion thereof, shall take technically feasible and reasonable measures, as expeditiously as possible, but in any case within 5 days after being served with a copy of the order, or within such time as the court may order, designed to--
(I) prevent its service from providing advertisements to or relating to the foreign infringing site that is subject to the order or a portion of such site specified in the order;
(II) cease making available advertisements for the foreign infringing site or such portion thereof, or paid or sponsored search results, links, or other placements that provide access to such foreign infringing site or such portion thereof; and
(III) cease providing or receiving any compensation for advertising or related services to, from, or in connection with such foreign infringing site or such portion thereof.
(ii) NO DUTY TO MONITOR- An internet advertising service shall be considered to be in compliance with clause (i) if it takes action described in that clause with respect to accounts it has as of the date on which a copy of the order is served, or as of the date on which the order is amended under subsection (e).

I'm not sure how to quantify the number of sites Google would be forced to deal with on a daily basis if this legislation were to pass, but I suspect the number could be quite large. Registering hosting and/or domains is a trivial task.

Cotton's proposal that immunity was provided to Search Engines and Ad Networks is laughable. Here are the bill's actual claims:
(A) IMMUNITY FROM SUIT- Other than in an action pursuant to paragraph (4), no cause of action shall lie in any Federal or State court or administrative agency against any entity served with a copy of a court order issued under this subsection, or against any director, officer, employee, or agent thereof, for any act reasonably designed to comply with this subsection or reasonably arising from such order.
(B) IMMUNITY FROM LIABILITY- Other than in an action pursuant to paragraph (4)--

It promises immunity... Except for repercussions due to not correctly acting on the courts orders in a timely manner. So not only is there no real immunity, but there's a burden placed on businesses to immediately comply or 'else'.

Moreover, imagine that later down the road you were unlucky enough to purchase one of the domains that had been blacklisted. In order to be listed in a search index, receieve advertising revenue or conduct payments, you would need to file a motion with the court to lift the ban. An innocent person, who has never been found guilty of doing any harm, would be required to jump through legal hurdles in order to exist on the internet.

(d) Modification or Vacation of Orders-
(1) IN GENERAL- At any time after the issuance of an order under subsection (b), a motion to modify, suspend, or vacate the order may be filed by--
(A) any person, or owner or operator of property, that is subject to the order;
(B) any registrant of the domain name, or the owner or operator, of the Internet site that is subject to the order;
(C) any domain name registrar, registry, or other domain name registration authority that has registered or assigned the domain name of the Internet site that is subject to the order; or
(D) any entity that has been served with a copy of an order pursuant to subsection (c) that requires such entity to take action prescribed in that subsection.
(2) RELIEF- Relief under this subsection shall be proper if the court finds that--
(A) the foreign Internet site subject to the order is no longer, or never was, a foreign infringing site; or
(B) the interests of justice otherwise require that the order be modified, suspended, or vacated.

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I'm going to continue paging through the bill, but I think this response is adequate to rebuke Cotton's assertion that this only effects "wholesale piracy websites outside of the USA". None of the parties I mentioned above were pirates, nor were they necessarily foreign entities.