I've not tried it, but I have heard of other turners doing it to make accurate cylinders. Don't see why it wouldn't work on spindle work (wood grain parallel to the lathe bed) if the plane's truly sharp. I'd want to be standing out of the line of fire just in case a catch pulls the plane from my hands, though. Although it seem in most cases, a catch would be a non-event. With such a limited amount of the blade exposed, it seems it'd be hard to get a bad catch. You do want to skew the plane at an angle though, or else you run the risk of exposing a lot of cutting edge to the wood at once. When doing a planing cut with a skew chisel, you're just exposing a small amount of the cutting edge to the wood. If you let a hand plane get perpendicular to the workpiece, you're potentially exposing 1 1/2" to 2" of cutting edge to the wood at once. That's a big bite, even if it's a shallow cut.
I don't think it would be a good idea on faceplate work (grain perpendicular to the lathe bed) due to the alternating end grain and face grain.