In preparation for upgrading to 2.3.5 I want to know if I need to do the database schema change or is it done for me?

You have to do it yourself. Find out the SQL file that match your database type under upgrade/2.3.5 named <db_type>_2.3.2_to_2.3.5.sql.
Run it once before you start up JForum.

If I make the schema change in advance, will 2.3.4 still run OK?

Yes, this time only add a new column user_twitter in jforum_users table, and its default value is null.
I think your JForum 2.3.4 will still work.