It's unlikely the FED does anything like this, but a company could easily do it, by either accepting USD deposits and issuing USD-coins in exchange, or simply allowing people to deposit BTC, convert it at the Bitstamp rate, and in the backend, convert the BTC to USD in order to cancel out the exposure.
I expect we will see USD-tokens in the not-so-distant future from credible third-parties. I think these will be useful, however, they still have problems, for example:
(a) the issuer cannot easily prove his reserves of USD,
(b) the issuer cannot easily post a "proof-of-intent" bond that acts as reserves for settlement of the options contracts.
The USD/BTC put/call idea
with settlement in bitcoin could allow one to hedge against the BTC/USD exchange rate completely outside of the traditional banking system and with 100% transparency. The counter-party risk, although not zero, can be made very small by using colored coins + multisig with neutral third parties + proof-of-intent reserves.