I think the residual lather helps, but I don't think its necessary. This AM, for example, I did a pretty thorough rinse before the cleanup. I think you're right that the Feather would be the go-to razor on this. Perhaps this is why I don't get as many shave off of a Pro Super blade as some others.
In any case, there are some places where I can do this and get excellent results. My neck can jawline, to be sure. I've had a tad more trouble doing this with my cheeks. Also, I find that the shave needs to be really close, and the beard reduced quite a bit before I can get away with this. While I say its my third pass, I confess I've done quite a few with the grain and across the grain passes on my chin area, sort of during the first pass, and with the blade at an obscenely big angle, to reduce the beard enough for the razor not to pull or hang up on the water-only clean up. For some reason, on my chin, this just doesn't lead to irritation or ingrowns.
http://www.en.nassrasur.com/razorcentral/secpass.html specifically mentions using a water-only second pass for a plain old straight razor shave. I don't know that I'd want to try that with a conventional straight, though.