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.
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.