One might think that equal owner/workers would be reluctant to go to war with equal owner/workers that were members of the same organization and industry but of different national states. Might countries come one day to be considered obsolete organizations? If countries did not exist they could not have a war.
I am wary of collapsing different issues into one or the similar tendency of believing that solving one problem will automatically solve others. The transition from hierarchical, top-down capitalist enterprise organization to democratic worker-coops is a big enough social achievement with multiple positive effects to focus our attention. But I dont presume it will solve international tensions and differences or necessarily dissolve the state/nation. Those are sepearte issues and problems for which societies will need to find solutions as effective on those domains as democratizing workplaces is on the economic structures of society. I can suggest that once workers achieve and become accustomed to real democratic control over their workplaces, they will be far, far less willing to give over control of politics to party professionals and that alone reduces war risks significantly.