Does Redux Use Persistent Data Structure?

Redux doesn't actually use any data structures itself. The "current state" value is whatever you return from your root reducer function. That could be a simple counter value, a plain JS array or object, an Immutable.js Map or List, or something else.

Redux is an architecture for managing your state. It doesn't use any data structure. It keeps the data structure which you provide to it, i.e., state. If you want to keep an eye in your store and want to go back to the actions fired then you'll have to maintain that in your state and handle that yourself. Some modules like redux state history provide that for you. You might as well want to look at implementing undo history with redux in which you'll find that nothing is persistent with redux but you'll have to make your app persistent by storing history. Redux devtools will give you the freedom of changing your state dynamically in the browser by going back in the history of actions fired.

I'm not sure I understand fully your question but

"In computing, a persistent data structure is a data structure that always preserves the previous version of itself when it is modified"

As far as I know redux is just a pattern and there is no persistant data structures associated with, unless you create and bind something yourself (like mongo event sourcing for example).