Check if document is part of Elasticsearch query?

It's a interesting use-case but you need to understand that Elasticsearch(ES) doesn't return all the matching documents ids in the search result and return by default only the 10 documents in the response, which can be changed by the size parameter.

And if you increase the size param and have millions of matching docs in your query then ES query performance would be very bad and it might bring even entire cluster down if you frequently fire such queries(in absence of circuit breaker) so be cautious about it.

You are right that, ES cache the stuff, but again that if you try to cache huge amount of data and that is getting invalidate very frequent then you will not get the required performance benefits, so better do the benchmark against it.

You are already on the correct path to use, scroll API to iterate on millions on search result, just see below points to improve further.

1. First get the count of search result, this is included in default search response with eq or greater value which will give you idea that how many search results you have based on which you can give size param for subsequent calls to see if your id is present or not.
2. See if you effectively utilize the filters context in your query, which is by default cached at ES.
3. Benchmark your some heavy scroll API calls with your data.
4. Refer this thread to fine tune your cluster and index configuration to optimize ES response further.