Catching falls is definitely one thing Microcenders are supposed to be for (when climbing rock, anyway), because suggested uses include backing up a belay, and self-belaying when top-roping. One of the advantages claimed in that application is that the cam is toothless, therefore it will slip a bit when loaded, reducing the shock load and damage to the rope.
Of course, that doesn't neccessarily mean much to us, as they are probably talking about use on dynamic rope. Interestingly, they recommend the device be attached directly to the harness with a carabiner, and it seems to me that could be problematic in forcing the Microcender into an undesirable attitude or position, whereas using a tether (especially a short one, as you mentioned) would allow some twisting and movement that wouldn't disturb the device, kind of like a swivel.
If Mr. Mumford wanted to test this, it would be great! However, I'm not offering up my Microcender for the experiment -- I'm too fond of it!