No. Persistent Data Structures are not mutable. The memory space of an older version is not rewritten, it is referenced by the newer version as a part of its definition. ie via composition. It can only safely do this if the data it references is guaranteed to not change.

x = 2 :: 1 :: Nil -- [2, 1]
y = 3 :: x -- [3, 2, 1]

In this example both x and y are single linked lists. y is a node with value 3 and a pointer to x. If x was mutable then changing x would change y. That's bad™ so its not allowed.

If you want to learn more about functional programming I suggest reading Structures and Interpretation of Computer Programs or Learn You a Haskell for Great Good