Viability of using this framework

Is Vaadin recommended to use in creating applications like tellering/accounting/financial/etc. which will make use of SQL database to request data about accounts from members and such with CRUD capabilities?

Yes, vaadin has SQL containers and there also exist addons to provide CRUD functionality.
But if you have some layer of business logic, then directly accessing the db is not a good idea.

But vaadin also has other containers helping you in such situations.