Is there an Eclipse plug-in that will allow me to graphically generate a data model, and produce from it a MySQL Database Script for generation of that database, and generate PHP code for simple add/change/delete methods?
This way I can focus on programming the business logic, instead of fussing with the details of the SQL code.
You should use what is called a framework or ORM. Kohana is a good one, as is codeIgniter, and Doctrine. You can specify your data models in one location and have the DB and code generated. I'm not sure about generating it from a UML model tho.
You can use this UMLtoPHP online generation service that can take as input a UML Eclipse class diagram and generate the corresponding doctrine file for you. With that you can easily generate a full CRUD php application using, for instance, symfony