Are ships flagged under state (A) considered the territory or under the sovereignty of (A)?
Is boarding such a ship by a state (B) which is not the same as (A) when (B) has an illegal blockade in international waters an act of war and thus a legitimate Casus belli?
I believe that the best answer is that you look at the 1962 UN Convention on the High Seas. That is where the idea of a "flag country" is defined under international law. The short answer is: no, ships are not sovereign territory when on the high seas, no matter how they are flagged or registered. The ship's registration does, however, determine how things like crime on board are handled.
The more important question that you ask is whether or not stopping a ship on the high seas constitutes a legitimate reason for going to war. This falls much more under traditional law, so we can look to history to know whether or not that is a probable outcome. During World War One, the Germans actually sank multiple ships, most famously the Lusitania, and that wasn't the reason why the United States went to war. Similarly, the North Koreans still have in their possession a US warship, the Pueblo, which was seized in the 1960s.
You predicate your question on the idea of an "illegal" blockade, but even that is open for interpretation. I'm not certain how you would distinguish between a legal and an illegal blockade. Blockades usually don't happen until a war has broken out, regardless. Obviously, countries with large navies are going to want to have blockades, and countries with small navies are not going to want them, so the Melian dialogue seems to apply in this case.
In the end, what constitutes a reason for going to war has nothing to do with the legality or illegality of seizing a ship. Such decisions are almost always made politically, and not because of the terms of treaties. Importantly, it also usually means that war is less likely, rather than more likely. Basically, countries do not want to be bound to go to war just because a ship is seized on the high seas, which happens all the time.
