This is the really important question that needs to be answered by future research investigations!

Currently, we don’t know just how systemic the effect of CNS fatigue is. Technically, since CNS fatigue refers to the ability to voluntarily activate the trained muscle, it could be 100% localized on that muscle, and may not affect other trained muscles. However, since the mechanisms that cause CNS fatigue to occur are still quite unclear, there could be systemic effects that cause CNS fatigue to occur in other muscle groups.

My hypothesis is that there is a primary mechanism that is muscle-specific (so antagonist training should work fine) but there is also a secondary mechanism involving aerobic contribution that is systemic. So if we train in such a way as to get very out-of-breath, then we might start to experience CNS fatigue that impacts on other muscle groups.