No, the immutability is only applied to the amount and references of the objects in the Collection, and does not address the mutability of objects you put in the Collection.
What Immutable list gains over the standard JDK Collections.unmodifiableList is that by using ImmutableList you are guaranteed that the objects referenced, their order and the size of the list cannot change from any source. With Collections.unmodifiableList if something else has a reference to the underlying list, that code can modify the list even though you have a reference to an unmodifiable list.
If, however, you want true immutability, you have to fill the list with immutable objects.