Using ddl triggers with in-memory tables
No, databases with In-Memory OLTP enabled do not support DDL triggers.  


  Both database-level and server-level DDL triggers are not supported with In-Memory OLTP tables and natively compiled modules.


You cannot create DDL triggers in a database where In-Memory OLTP is enabled since the code path required to run the trigger would interfere with the In-Memory functionality.  The workaround is to put all your In-Memory OLTP tables in a single database without a DDL trigger, and the rest of your tables into a separate database without memory-optimized tables, and enable the DDL Trigger there.