The success will depend on the "strength" of the backing, and this is not addressed in your system.

If someone wishes to attack the currency, the first place is to attack the backing.  So even if the backing hasn't failed yet, it stands to be very weak unless there is some mechanism to make it robust.  Weak backing does not deserve the term backing.

Anything other than physical coins that have bullion value have a chance of failing, but some instruments are much stronger than others.  A personal check vs a cashier's check are worlds apart in terms of their strength.  Even though neither is absolute, I would want the system to be roughly as strong as a cashier's check in terms of the level of certainty that I'll be able to redeem it.

It is theoretically possible to make it decentralized using dead drops or if some anonymous trust mechanism can be strong enough.  I think this could be a fruitful direction of exploration.  Figuring out how to set up anonymous, decentralized, guaranteed redemption is the hard part, not how to set up auctions and create the currency.