He wouldn't need to buy all of them. If his purchasing streak pushes prices up so high, or so fast, that nobody will sell them or use them, then for all practical purposes, bitcoin is dead. A currency with no current is not.
A currency with no current is a store of value just as an atom that sheds no electrons is still potential energy. Bitcoin is money, not a currency traded for a single commodity at the highest market price on a universal exchange. Bitcoin is not more or less dead whether a bitcoin can be sold for $4 USD or $265 USD. People tend to hoard coins as prices move up and they tend to spend coins as prices move down. Bitcoins are commonly exchanged for values that are unrelated to a fiat currency. The market would have "current" as it finds a balance between hoarding and spending.