Hi anonymous user, welcome to Microsoft QnA forum.
Adding a Business Critical Database to General Purpose Elastic Pool is allowed as any other database but once you add, the business critical database will be scaled down to General Purpose Elastic Pool. That means storage limits and cost are applicable as per the General Purpose Elastic pool only.
After adding the database, if you go back and check the activity log of Business critical database, you can see the changes as below:
Yellow - Old values
Green - New values
Again if you try to scale up the database from General Purpose Elastic Pool to Business Critical, this database will be removed from the elastic pool.
Please let us know if this helps.