I gave it a shot and it appears to work as expected.

  sqlite> create table a (id int primary key, j json);
  sqlite> insert into a values (1, '{"hello":"world"}');
  sqlite> create index idx_a on a (json_extract(j, '$.hello'));
  sqlite> explain query plan select * from a where json_extract(j, '$.hello') = 'world';
  QUERY PLAN
  `--SEARCH TABLE a USING INDEX idx_a (<expr>=?)
  sqlite> explain query plan select * from a where json_extract(j, '$.foo') = 'world';
  QUERY PLAN
  `--SCAN TABLE a