Hi, this is a very interesting idea and I highly encourage you (or anybody else) to attempt to code it up.

If I am understanding your idea correctly, this would be quite similar to ICBIT.se, the existing bitcoin futures exchange, which has been trading for some time.  Originally you could deposit and withdraw both bitcoin and dollars there but they have since removed the option to transact in fiat directly.  So now it's just bitcoin in and bitcoins out, trading on virtual dollars, much like your idea.

Of course the difference would be that yours would be decentralized, with no fees for the centralized owner to charge, and no third-party credit risk.  Also, yours would be more like a "spot future" which would be continually settled, unlike the futures on ICBIT.se which settle every month.

I can think of no technical or commercial reason why this idea couldn't catch on and perhaps eventually become the de facto spot market for bitcoin/fiat ... with the following catch: other centralized exchanges dealing in btc/fiat that actually transact in fiat will still be necessary somewhere.

If someone has btc and needs dollars, or to buy something in dollars, your exchange can't help.