The simple answer is no. Installing the
JIRA Agile extension / plugin adds issue type Epic (and a few others) to the base JIRA installation. None of the features (epic links,epic filtering by backlog, epic burndown charts, etc.) work for other types of problems.
It is recommended to start by adapting the process to use the new problem type.
Now there is nothing to prevent you from associating a custom field (when used for specs, development, and test information) with an Epic issue type to provide the same functionality as the new feature.