Frankly, I think Koskenniemi is way off on this point. Rather than International Law serving as an instrument through which the particular is made universal, I'd argue that International Law serves as the opposite. We'll take the example of the Iraq war. Now a sophisticated Marxist analysis must of course view the war in all its conjunctural specificity. It is a concrete event in and of itself. However, the concrete event is only really to be understood as a manifestation of a universal 'structure'. Thus the war should be seen as an imperialist war, and imperialism must be seen not as particular strategy adopted by a 'cabal of neo-cons', but as a structural relation inherent in the world economy.
“International law may act precisely as an instrument through which particular grievances may be articulated as universal ones and in this way, like myth, construct a sense of universal humanity through the act of invoking it. From such a perspective, the project of universal justice appears as a horizon at the intersection of a public realm of states regulated by international law and the civil society reaching beyond sectarian interests. That this intersection appears only occasionally, and even then in connection with events of exceptional magnitude, even scandal, is an aspect of the difficulty that any fundamental challenge to the iron laws of power must imply.”
This means that the Iraq war should be seen as a concrete manifestation of 'universal' social relations. But when Iraq is viewed through the prism of international law all of this disappears. The war is condemned for being 'illegal' (and this is questionable in itself), but legality must always refer to a highly specific set of events. Thus what is condemned is not imperialism, or even war in general but this particular war.
Whilst it is no doubt true that opposition to the war based on international law might mobilise large numbers of diverse people this is not the same as setting the war up as a universal. In fact part of the reason that a legalistic opposition to the war is able to gain large amounts of followers is precisely because of the specificity of analysis. Opposing the war on legal principles means one does not need to carry out any broader analysis of why such wars happen in the first place, and certainly does not commit one to an opposition of the domestic status quo.
Furthermore condemning the war as illegal opens up questions as to whether it is therefore ok to support imperialist wars that are seemingly legal. Considering the fact that 'legality' to a large extent structurally favours 'power' over 'justice' (if one can even invoke such a term) is a nail in the coffin for this thesis.
Ultimately legalistic opposition serves the opposite of what Koskenniemi suggests. The illegality of the war will always be confined to 'the facts', this is even more the case with international law, where norms are freewheeling and hugely context specific. Furthermore, opposition rooted in international law means that once a country is given legal authorisation to head in and start the bombings opposition 'dries up'.