As of SQL 2016, the database engine automatically updates statistics for memory-optimized tables (documentation here), but recompilation of native modules must still be performed manually. But hey, that’s way better than SQL 2014, when you couldn’t recompile at all; you had to drop/recreate the native module. And natively compiled stored procedures don’t reside in the plan cache, because they are executed directly by the database engine.
This post attempts to determine if the requirement to manually recompile native modules is any different for AG secondary replicas.
The results are interesting.