Is it possible to add cookie to the request while using IRestFulClient from HAPI-FHIR?
This could be done quite easily by creating a custom interceptor which adds a cookie header. You can see an example of a client interceptor which adds an authorization header here. If you copy that code but change the header from "Authorization" to "Cookie", then register the interceptor by calling
client.registerInterceptor(interceptor);
..you will get that behaviour.
Incidentally, if you create such an interceptor and wanted to share it back with the project, we'd love to have it! :)