Can SQL Server Transactional Replication do this?
I believe your DBA is referring to Publishing Stored Procedure Execution in Transactional Replication.

With Transactional Replication you have the option to published the definition of the stored procedure or the execution of the stored procedure.  Publishing stored procedure execution can provide significantly better performance for large batch operations since only the procedure execution is replicated, bypassing the operation being sent to Subscribers as a large, multi-step transaction.

If you have anymore questions please let me know. I hope this helps.