I have transactional replication set up on SQL 2008, and the article in question has "Copy nonclustered Indexes" set to TRUE.
If I add a non-clustered index on the publisher (using CREATE INDEX), will that push to the subscriber immediately?
Or do I need to run a snapshot?
You'll have to push it to the subscriber yourself. "Copy..." only applies to the snapshot.
From MSDN : Frequently Asked Questions for Replication Administrators
How do I add or change indexes on publication and subscription databases? Indexes can be added at the Publisher or Subscribers with no special considerations for replication (be aware that indexes can affect performance). CREATE INDEX and ALTER INDEX are not replicated, so if you add or change an index at, for example, the Publisher, you must make the same addition or change at the Subscriber if you want it reflected there. You would need to push a snapshot. You'll probably find it easier to simply create the index on the subscriber if the index is needed there.
