Yeah why not, in fact, most of the search applications (like e-commerce) search are powered by search DB(Elasticsearch or Solr) but they are backed by RDBMS(this is the source of truth), Also Elasticsearch index building from these Databases are very common.
RDBMS are good for relational transactional systems but if you want to speed the search queries(instead of creating huge indices in RDBMS) it always makes sense to use Elasticsearch(which also is very performant in case of filters and aggregation).
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