"Wouldn't the presence of self-awareness be a prerequisite, so just about every device should fail, before even getting to the actual test?"
I'll reply to you.
I think I just decided that Siri is what a Loebner Prize contest bot would look like "if it was developed for real with some money behind it."
http://en.wikipedia.org/wiki/Loebner_contest
In that contest, they "waste time" trying to trick the bots with edge case questions. For Siri, you know it's a bot, but you ask "is this answer useful". To me that is the spirit/next-gen spirit of the Turing Test. "Is this answer as useful as a person? Better?"
Now, to Self Awareness. It's not all that hard to put in a meta module where the machine "knows" about itself. It could have its specs, but also more general statements like "I'm not so good on long sentences."
Sometimes those kinds of statements "aren't as hard as we pretend they are to feel superior". As a college kid will tell you if you give him a beer for his time, about the same 100 questions show up in intermixing sets of 12. But once you know "who you are" (and what you "don't know"), then it kinda reduces down until new experience changes some of the answers.
For this reason, I considered the old Pentium I chip an extremely important tool for "AI" that I have never seen used in a special way. Because as far as I know, it was the only chip commercially famous (not a limited edition or knockoff) that had provable logic errors.
Crunch. Logic Errors are the "unfortunate hallmark of being human". So we developed all these "social skills" to maneuver around the errors. Systems design, to just getting sleep.
So if you used a P1 chip for AI, then gave it a module to "be aware that it was flawed", when it "tried to do its duty" it could do checks and inform the user "I am sorry, but that requested process will likely trigger my logic failed circuit. Do you still want to do that or find some other solution?"