I think you could say that. Another way to look at it would be to say it's about organising your code in such a way that side-effects don't really matter. For instance, if only I have access to a reference, then I'm free to update it without risk of disrupting anyone else's world view. You could say that there is no side-effect from my update because no-one can observe the change.

This is nice for functional programming because it gives you the performance of mutable state and destructive update, but in a way that is 'pure', or side-effect free, from the outside.