IDP should work without problems even if you do not have ElasticSearch installed in your system.
IDP has its functionalities available for semi-automated operations (i.e. automated operation but manually triggered by an operator) and then it can go fully automated with the help of Process Automation where you can configure Processes to automatically be executed at a point in time or periodically.
And for this last option, you will need the Elastic engine as that is a requirement of Process Automation.
This fully automated manner is not required and IDP will continue to work but it provides a great added value to the solution.
You can see the differences in the UI below
Hope this explanation was helpful to you.