No. Doctrine 2 does not give rise to anemic domain model designs.
If you explore the D2 code you will find that D2 uses reflection to hydrate and persist it's entities. No getters/setters are required for D2 to work it's magic. Not even the constructor is called. D2 does not care how you model your domain.
It's also fairly easy to structure an application to make the domain model independent of the persistent layer.
Doctrine\\Product.php (extends Model\\Product)
Doctrine\\ProductRepository (implements Model\\ProductRepositoryInterface
InMemory\\ProductRepository (implements Model\\ProductRepositoryInterface)
You can pretty much do whatever you want in the Domain Model layer. And then persist with Doctrine or pretty much any other reasonable persistence library. You can even chose which library to use at run time.
The anemic domain model is basically a result of the types of applications which end up being implemented in PHP. PHP is mostly used for CRUD type applications. Business logic is usually stored in services of some sort.
Here is the challenge: Post a link to any PHP application out there that does NOT use an anemic domain data model. I have seen one or two very simple examples but nothing in production.