Yes, this is implemented as an API1 call which can be called via the JSON API. You can find how something is called by looking at the page which the <form> references on the page of cPanel where the action is being taken.
In this case, it's /usr/local/cpanel/base/frontend/x3/optimize/dooptimize.html:
<cpanel OptimizeWS="optimizews($RAW_FORM{'deflate'},$RAW_FORM{'deflate-mime-list'})">
Here's an example of how to call it:
https://<HOSTNAME>:2083/cpsess6366747/json-api/cpanel?cpanel_jsonapi_module=OptimizeWS&cpanel_jsonapi_func=optimizews&cpanel_jsonapi_apiversion=1&arg-0=list&arg-1=text/html%20text/plain%20text/xml
There's documentation available in cPanel's API1 docs:
OptimizeWS Module Documentation
