Is it possible to create a workflow or jquery function within the list's page that would allow a user to automatically be signed up for the built-in sharepoint alerts on any item they themselves create in the list? This can be remedied with a workflow to create our own custom alert emails, but would like to try to implement the built-ins. Is this doable?
In SharePoint Designer, create a workflow that sends an email to the creator of the item on creation and on item change. This is out of the box functionality.
but would like to try to implement the built-ins
Not sure what you mean by that.. unless you mean out of the box.