The short answer to you question is that I believe language copy actually kills the live copy relationship so no roll outs will impact the copy.
In general language copy is intended to be used to create language copies when you want to do something like manual translation and you simply creating the initial copy of the site. Language copy does not create a relationship between source and target the way that Live Copy does. So in the normal scenario where you creating a language copy of your master there is no rollout - you have to maintain any synchronization between the source and target manually.
In the use case you described where you create a language copy of something that is itself a Live Copy of something else it looks to me as if Language Copy creates the desired copy, but then removes any LiveCopy relationships as the content is copied (both LiveRelationship mixin and the LiveSyncConfig node if present).
What I think you actually want to do is create a live copy not a language copy if you want a rollout impact.