Please ignore the disingenuous answer regarding the ten-thousandth of an degree answer. The face, or legs and underarms, are not a smooth surface and in the process of shaving the blade can change angle by whole degrees, which, at worst, will only affect the closeness of the shave.
The sharpest any blade can be, ideally on a microscopic level, is one atom thick. The moment a razor meets skin and stubble these atoms are removed and after a few uses the blades sharpness, and indeed usefulness, is drastically reduced. Which usually results in disposal of the old blade in exchange of a new one.
The idea behind the Save-A-Blade is sound, and has been practiced by barbers for centuries, as drawing a blade down a leather strop heats it up and pulls the atoms back to the edge, and we call this honing.
But getting to the meat of your question; Does it work on disposable blades?
It probably will at first, but you will quickly see diminishing returns as the stropping device in the unit will not ever be able to contact enough of the blades to efficiently pull these atoms down indefinitely. Then taking into consideration the cost of batteries for the honing unit it quickly becomes more cost-effective just to pick a brand of cheap one piece disposables, that are comfortable to use, and change them out weekly.
While individual opinions may vary, it's pretty much a given that the shaving hierarchy is, Straight Razors, cheap disposables, expensive handle units with even more expensive replacement cartridges, and finally electrics.
If you really want to give your fiancee a shaving gift, find him one of the old antique safety razor units, with replaceable double edged blades. These are as close as you can get to a straight razor shave, with the convenience of swapping out the blades to insure sharpness. And with a bit of practice, he can achieve a better shave than any disposable unit without the fear of mortally wounding himself.
.it does work.