Not really - the ability to use Bitcoins to transfer useful amounts of money is very much dependant on their value and vice-versa. They probably don't need to be anywhere near the current price in order to support the current transaction volume, but I doubt $0.01/BTC would work.
True - I was reaching out for an extreme. When the price dropped to less than $3 from ~$35 I think it was close to losing its critical mass, but I think as long as the price is at least $10-20/BTC, the infrastructure backing it as a medium of transfer will still exist.
That's a separate set of characteristics from talking about Bitcoin as an investment.
Tulips, when the price crashed, were still pretty flowers.
Bitcoins, if the price goes to $0.01/BTC, still have those characteristics you described.