Highly unlikely. It's more likely that the value of bitcoins goes up slightly with each minute loss of bitcoins, and people start using them in smaller fractions.

How can the market adjust in a vacuum of information?

Yup. That's a feature of currency systems that are pegged to a commodity. The difference is that instead of coconuts or gold, the scarce commodity is a bunch of random numbers.

The are many problems with such systems, which is why the entire planet moved away from them starting about 100 years ago. Just like the initial users of BitCoin who are sitting on millions of the things are limiting the bitcoin supply in order to slowly sell them for real coin.