It is possible, but it depends on how you're doing your data migration. As an example, if you're using the Migration toolset to migrate your data over, and your feature-linked annotation is related via a global id, we can bring the data over as related data during the migration.
Other tools and methods can be used, but the biggest challenge is ensuring you're properly creating the consolidated annotation class in the target environment before you migrate the feature-linked annotation to the new database. That's not to say that the process is easy, but it is possible, and most data conversion vendors have cretaed special tools and processes already established to prepare, validate, and migrate feature-linked annotation.
If you have any broken or invalid annotation in your source data, you will need to get that cleaned up first.
