In two words: yes, they can.
Eric Evans in his book tells about a "thread of continuity" inherent to entities. In layman terms, an entity can be POSTed by a front-end as JSON, get converted into a DTO by a framework, then into a domain object, then into a DTO again and then finally get stored in a database table. During all these transformations the entity will be easily distinguishable because it possesses one or more unique business ids.
With this in mind, aren't some forms of immutability a form of another thread of continuity? Imagine copy-on-write: all of the immutable object's copies are formally different objects representing it at different points of its lifetime. Yet, there is a unique id allowing us to say it's the same entity.
Now, let's talk about the "extreme" form of immutability: read-only objects. Can an entity be a read-only object? Sure, a good example is a credit card statement.
Summing up:
- One entity can exist in many forms. In fact, you will almost always have multiple representations of your entity in a program without being aware about it.
- A true requirement an entity is an existence of a unique business identity (not a surrogate id that is used for technical purposes) that makes it distinguishable from other entities.
- Entities can be immutable, whether we talk about COW or read-only objects.