Is it possible to perform a full text search query operation via either the
SQL interface? Or the REST API interface?
And does this (or the Java API) automatically leverage Lucene indexing as
per the documentation example for a TextQuery? Or are there other specific
operations or configurations required to use the Lucene indexing features?
REST API does not have such option, but you can write your own compute task
(that uses Java API) and call it from REST . It's not possible to use
Lucene search from SQL interfaces.
To use full text search you need to annotate fields with @QueryTextField 
and add to indexed types .
Ignite will automatically manage Lucene indexes and you'll be able to search
with a TextQuery.
Also, please note that Lucene indexes work only in in-memory mode .