Can an Idoc be deleted from the system without any trace ? It can... but do make sure this is handled with care. Transaction WE11- delete Idocs. Sap has made it quite easy to get rid of Idocs for a certain message type and with a given creation date/time.
This could be quite useful where Idoc processing is concerned. Inbound runs that went wrong can be corrected, Idoc's that are no longer needed can be disposed of, a single isolated problem Idoc can be removed. You can (since 2014) supply an individual Idoc number to make that single Idoc disappear - without a trace. Except maybe a gap in Idoc numbers. And a mention on the system log ?
A note for scheduled use
when Idocs are cleared as a means of archiving, it is likely the number of Idocs to be removed will be quite large. As the delete program is not build for this - database rollback problems can be expected. For regular removal of Idocs - use Idoc archiving.
WE11: Handle with due care!