From what I remember and quick look at code output of administration menu is hardcoded into menu-header.php, which in turn is hardcoded into admin-header.php. In other words not something you can get rid of easily and painlessly.
Note that admin menu can be collapsed to quite thin toolbar, so if your main need is to recover that space then easier and less confusing to user might be to collapse it by code (would probably need a bit of JavaScript, not my area), rather than remove it completely.