I've found my own work-around:
In the library settings, changing "require documents to be checked out before they can be edited" to "No" whilst performing the upload means they are not uploaded as "checked out" and the time-stamp is retained.
In the library settings, changing "require documents to be checked out before they can be edited" to "No" whilst performing the upload means they are not uploaded as "checked out" and the time-stamp is retained.