Starkler - In a word (as per the NZ site) a "feeling" is what you get. Although you won't get a true stereoscopic view in the proper sense because, as you say - objects are just too far away to get any real separation), just the fact that your two eyes are receiving data leads to a sense of depth - and moreso than viewing through just a bino attached to a monocular scope. I'm frustrated that I don't have, and can't give you a plausible technical explanation as to why it's so - Mark has a good grasp on a technical level how it works differently - and I invite him to post a response to this question here. Nebulous regions such as M42 and NGC2070 just have far more contrast for some reason - especially with twin OIII's on. As per all of the sites that rattle on about the virtues of bino vision - owners all universally have trouble putting the "it" into words.
It's just one of those things you have to see. SPSP will be the go if you can make it!