Going with my personal favorite backstory for this test, we should expect to terminate every AI in the test, so the latter part of your comment has a lot of weight to it.
On the other hand, an unfriendly AI should figure out that since it's going to die, useful information will at least lead us to view it as a potentially valuable candidate instead of a clear dead end like the ones that threaten to torture a trillion people in vengeance... so it's not evidence of friendliness (I'm not sure anything can be), but it does seem to be a good reason to stay awhile and listen before nuking it.
Eliezer proposed in a comment:
>More difficult version of AI-Box Experiment: Instead of having up to 2 hours, you can lose at any time if the other player types AI DESTROYED. The Gatekeeper player has told their friends that they will type this as soon as the Experiment starts. You can type up to one sentence in your IRC queue and hit return immediately, the other player cannot type anything before the game starts (so you can show at least one sentence up to IRC character limits before they can type AI DESTROYED). Do you think you can win?
This spawned a flurry of ideas on what the AI might say. I think there's a lot more ideas to be mined in that line of thought, and the discussion merits its own thread.
So, give your suggestion - what might an AI might say to save or free itself?
(The AI-box experiment is explained here)
EDIT: one caveat to the discussion: it should go without saying, but you probably shouldn't come out of this thinking, "Well, if we can just avoid X, Y, and Z, we're golden!" This should hopefully be a fun way to get us thinking about the broader issue of superinteligent AI in general. (Credit goes to Elizer, RichardKennaway, and others for the caveat)