I very much like the idea. I think all things mentioned by rummaker could be implemented, this would just require more skill and scouting smartly.
This would be nice. You can see a lot that could be kept hidden.
Except hiding the race... openers are way to big of a factor in this game that it would make random players have to much of an advantage.
Except not really, because if you know someone is chaos, you can swordwrath mass. Random would actually make scouting even more useful, and would provide a useful counter to an anti-chaos opener (or vise-versa, but I currently know of no such chaos opener that is "too powerful" for Order).
With more races though, random would also have the setback as to playing a race you are not ultimately comfortable with. Right now, with only 2 races, it's fair to say I have equal skill in each. However, it's really hard to open with chaos against a good, aggressive yet controlled order player. This is why I'm prompted to go random sometimes. Maps are random too, and that will also affect this decision. I may be alone on this, but when you start putting down your "play-to-win" chants and actually play straight against chaos you'll see the opener is actually the weakest link in the empire.
I've said too much as it is, but you as a SC2 fan should of all people understand why this is a big deal.