Not organising labour in the imperial core is certainly not going to do the periphery any good, or do imperial core workers any good either. Organised labour has the power to force concessions from the bourgeoisie who depends on their labour. They can't really apply pressure to the periphery, only the bourgeoisie has that ability. And even if organised labour in the core wanted more imperialism the bourgeoisie is already robbing the periphery as much as humanly possible so it would be hard to see how it could get any worse.

This doesn't mean that unions in the imperial core can't have really atrocious politics. Many of them do and are perfectly happy to throw the periphery, the lumpen, minorities and even other unions under the bus to get something for themselves. Plenty of critique can and should be directed against "moderate" unions in the core who have forgotten their radical roots and has become part of the machinery maintaining the capitalist order rather than an opposition to it.

But the thing is that bad unions are arguably better than no unions. A bad union has a membership and an organisational structure that can be radicalised by changing material conditions and just buy existing they reproduce the idea of organised labour even being a thing to begin with. Having to build all of that from scratch takes an enormous amount of time, effort and blood.