"There is no deep copy in java," but does it matter for list of Strings?

Let's say I do:

public List<E> gimmeAList(List<E> original) {
    return new ArrayList<E>(original); // this is a shallow memcopy.
} 

I try to modify the new list, but since Strings (or any immutable object) are immutable, doing something like: gimmeAList(something).get(0).replace("a", "b"); doesn't ACTUALLY seem to change anything in either lists.

So in this case, am I allowed to just assume (for immutable objects in a list) that new ArrayList<E>(original) is guaranteed to be, for all intents and purposes, basically a deep copy?