Could BitCoin ever be backed by Gold or some other commodity in the following fashion? And would it be desirable to do this?
Assume for the sake of argument that all 21 million coins were in circulation as of just today.  Suppose some rich reputable entity (Bill Gates or the Pope) bought up all bitcoins at market price (29 cents) for $6,090,000.   Some amount of gold is purchased, placed in a vault in Switzerland, and the coins are sold back to the public for some amount of money which the market will bear in such a manner that Bill or the Pope take no loss or gain.  Does that back the currency so that it is tied to the price of gold, similar to the way that everyone seems to want the US to have stayed on the gold standard?

Clearly I have not thought this through, but is there way to later back a fiat currency, or must it be done from the outset?  Further, is it desirable to do this?