I'm thinking about copying my text searchable content to Google's BigQuery and then perform full-text search using BigQuery API.
Does Google BigQuery support that scenario?
I could not find "search" command in Google BigQuery API: https://developers.google.com/bigquery/docs/reference/v2/
BigQuery support a collection of RegEx and String query functions, making it suitable for text search queries across STRING fields. However, there is a 64k per row (and field) limit for each BigQuery record, so it may not possible to support a totally unstructured, unlimited size, document text search case.
For a full text search capabilities in an App Engine application, I would suggest looking at the new Search API:
