There are really two issues here:
1. Making your article think that it has a Wikidata ID
2. Pulling data from Wikidata
There are a few potential ways we could trick an article into thinking it has a Wikidata ID, but adding one to the query string is definitely the easiest. If we really wanted to, we could write a new parserfunction that would allow you to permanently embed a Wikidata ID into an article (via something like {{WIKIDATAID:Q1234}} in the wikitext), but that would be a lot of work for little gain. Pretty much any other solution would lose the ID whenever you save the page (since it's recorded as a page property).
As far as dynamically pulling data from Wikidata into your local wiki, I don't really think there's any sane way to do it. The way we got rid of making API requests on every load was to communicate with Wikidata's database directly on page save. Since your local wiki isn't on the cluster, it doesn't have any way to communicate with Wikidata's database directly. We could reimplement an API-based system just for testing, but that also seems like a lot of work for little gain.
If you provision the WikiGrok role in Vagrant, you get a local Wikidata repo and client, so you could theoretically populate your own Wikidata with test data, but I imagine that would be a bit tedious. Maybe Max has some other ideas.