I am currently using Microsoft Azures elastic pool to allocate resources to my databases as needed, however for my purposes at the moment the cost is too high for the amount of traffic the databases are handling. My question is if I removed the databases from the elastic pool and delete it will I need to update the SQL queries in my codebase?
I would not expect you would need to change any query. Elastic pools are meant to be for managing the pool of resource to distribute among the databases as and when needed. Moving the database in the pool as well as out is supported which does not indicate any need to update the application (or query). I would suggest move a database out from the pool and test few queries to rule out any 'What If' in the mind