ALTER COLUMN, trading a DOMAIN for its base datatype

I'm (still) trying to transition out from under the uniqueidentifier
contrib module to the native uuid datatype. I seem to be able to create a
domain for uniqueidentifier:

CREATE DOMAIN public.uniqueidentifier AS uuid;

and then use pg_restore to reload my data without the contrib module.

I'd like for my final step to be to

ALTER TABLE foo ALTER COLUMN my_uuid TYPE uuid;

... Is PostgreSQL smart enough to not have to rewrite the table and simply
shed the domain for the underlying datatype?