Is ANALYZE useful immediately after creating an InnoDB index?
CREATE INDEX does not issue ANALYZE TABLE.

When it comes to InnoDB, running ANALYZE TABLE is kind of useless. Why ?

I wrote this post From where does the MySQL Query Optimizer read index statistics? 2.5 years ago.

In it, I explained that InnoDB can overwrite statistics by means of just running queries. The Query Optimizer will do depth searches in BTREE indexes and take guesses at the cardinality of index column combinations. In a relatively short time, I would say that index stats can get stale. This applies to older versions of MySQL 5.

From the ANALYZE TABLE Documentation for MySQL 5.6, InnoDB's stats are persistent by default. Thus, running ANALYZE TABLE on InnoDB tables for MySQL 5.6 actually means statistics are computed and will only deteriorate via heavy INSERTs, UPDATEs, and DELETEs.

As for you question, I say : CREATE INDEX does not issue ANALYZE TABLE automatically.