DOES THE SHAKE SHARP'S HONE MAINTAIN OR IMPROVE A STAINLESS STEEL BLADE'S PERFORMANCE?

Short answer: Doesn't look like it.

While a minority disagrees with them, I've long read reports from guys who said stropping and honing blades just does not work for them. In fact, it is widely reported that using traditional strop devices actually DEGRADED the quality of the shave. 

In my experience, these guys are correct insofar as they're talking about modern stainless steel blades, which they almost always are. While carbon blades are maintainable with post-shave drying, stropping and honing, the very few times I tried the same routine with stainless blades, the results were either inconclusive (meaning I noticed no difference) or the next shave was slightly but noticeably worse. 

Now that I have the Shake Sharp, and despite saying I'd never use it to hone a stainless blade, I figured it was the best time to put the idea to bed one way or the other. I used a perfectly usable Big Ben blade (on it's 3rd shave and starting to drag just a bit) with the built-in hone. Result: the fourth shave was considerably degraded. 

I am no expert and don't want to be but the only guess I can come up with is that the multiple bevels common on modern blades are screwed up when the blade is treated like a vintage carbon. I can't think of another reason why a stainless steel edge would go from "used but still OK" to "definitely worse," whereas carbon blades - which I don't think were as complexly beveled - invariably improve.

While the Big Ben stainless and the Shake Sharp are a fantastic shaving combo, I've confirmed my gut feeling to avoid using the Shake Sharp's hone to work over stainless blades. If other guys can perceive improvements from honing stainless, I heartily say, more power and better shaves to them.

My review of the Shake Sharp itself here.