The answer to your last question is yes.
To answer the general question: Firstly, result set and JSP should never be used in the same sentence. Write model classes that do all the database access completely separated from any UI aspects. The data should be copied from the result set into
Java collections/beans as appropriate, and the results sets closed as soon as possible.
Basically, the UI should know nothing about the database, and vice versa.
Controlling the action of the model class(es) is the job of the page controller. Once the controller gets the collections, is can place them onto the request as scoped variables and forward to the JSP page where JSTL/EL can take over the task of creating the HTML for the dropdowns.