If a country were to hypothetically set the length of time for a copyright to expire (and thus enter the public domain) to one second, does that make it legal to freely distribute any work of art produced in any other country at any time, within the borders of that country?
If in your example you assume the country is not subject to any treaty obligations whatsoever, then that is certainly something that country could do (though it would be easiert to just abandon copyright protection altogether). (A sovereign state can set their own laws by virtue of being a sovereign state.) In the early days of copyright, such efforts were not uncommon. The Kingdom of the Two Sicilies, for instance, was notorious in 19th century Italy for disregarding the copyright of other states. This was a deliberate policy choice that led to a burgeoning reprint business. Giuseppe Verdi was repeatedly warned by his publisher not to bring any of his scores to Naples for that was tantamount to having them spread across the world. Needless to say, when the first international copyright treaty was adopted between Austria and Sardinia (in 1840) and they invited the rest of Italy to join, the Two Sicilies were the only state to refuse.
Later on, the industrial heavyweights of the world have of course made sure this doesn't happen. The Berne Convention today has roughly 180 member states and there are several other copyright-related treaties in place as well (WCT, WPPT, TRIPS ...). Simply put, the strategy consists of two elements: First, no one gets a trade agreement without ensuring and properly enforcing the IP rights of foreigners. Second, if you don't protect our authors in your country, we don't protect your authors in our country. This has led to a fairly high standard of protection across the world.
In other words, if a country did this and a citizen of this country built a server filled with recent Hollywood movies, would users in that country legally be allowed to download those movies, and would the US have any right to seize and shut down that server (as they have done with torrent sites in the past)?
In purely legal terms, you cannot simply seize property in foreign countries. You always need a country that cooperates (is required to cooperate) with you, be it based on international law or as a "courtesy". If, hypothetically, there were some super-rogue country that for some reason is completely autarch and doesn't want to do business with the rest of the world, you couldn't force them to let you seize anything. (The military surely could ...)
However, even then, the operator of the server in your example would have some trouble of his own. Because if you operate a server in country X and offer Hollywood movies, without permission, you would expect that the rest of the world can download these movies as well, either directly or through a VPN service. In many countries, that would be enough to bring the action (the communication to the public of the content, see eg WCT, art 8) within the purview of their own jurisdiction. Which, in turn, means that the site operator should better not leave his country any time soon.