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
[1]: https://www.sqlite.org/expridx.html