Approximate KNN search with filtering vs. exact search after the filtering

Suppose I want to use KNN search to search for best matching documents (represented by their high-dimensional vector embeddings) belonging to a particular user.

As explained here, the approximate search (i.e. using HNSW) will filter out the documents of other users during the search itself. This seems to suggest that the search will have to encounter and discard all documents of all users that are as good or better match as the worst match in the result of the query (i.e. the Kth nearest neighbor for the user of interest).

When there are thousands of users, is this approximate KNN search any faster than the brute-force exact KNN search among the documents of the user of interest?

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