When Monarch writes out to a file like .accdb, it creates the file first of all, and then writes row after row of data to it. To write the data into the file involves lots of file system operations, so the closer and faster the disk is the better the performance.
Moving a file from one disk to another is handled perfectly well by the file system, without Monarch needing to be running to do it.
With Monarch, you could write a batch file to run the project export, and then copy the file to the remote location, or with DataPump you can set up a "Copy" or "Move" distribution in the XPRJ editor dialog.
DataPump distribution methods also include SharePoint, email, FTP, RSS...
How automatic do you need (or want) it to be?