The answer is No.
Because you know SAP has stored all data in table level, and when you run a transaction, SAP reads the data from the table and it will show you the data from this table.
If you press F1 - Technical settings in MM04 (on changes output), you will find the table CDHDR.
That means system is searching for the data which is exist in table CDHDR (and the correspond table CDPOS). So it is clear if you archive the all data from these tables, so system will not able to find any data from these tables. So system can;'t show you any log in MM04 or MM03-Envoirement-Changes log.
You can't see these t-code's changes logs, which t-codes are searching data from these (CDHDR and CDPOS) table.