As far as I can see, it requires several calls to publish or unpublish a product, i.e. 1 + [number of publications] calls, so 4 calls if you have 3 publications, one call for getting the publication ids, and then one call for each publication you want to publish product on.
Is there a more simpel way, e.g. as the deprecated "published" parameter on the product? It would be nice with a publish-on-all-publications mutation.