The USD will collapse. Left to the devices of the USG/FED sure, they'll prop it up, inflate it, kick the can as long as possible, wrecking the economy every step of the way.
The thing of it is, however, is that it's not JUST at the discretion of the FED.
Remember the founding principle of bitcoin and virtual currencies being "faith based" no matter that it's backed by math? Joe and Bob *trust* one another per transaction which gives the unit of trade its intrinsic value, right?
Well, the more bitcoin is understood based on what's already happening and widely accepted, the higher the increase in mainstream adoption because more people will be putting their *faith* in the math backed invisible "virtual" currency over and above rectangular sheets of paper and metal coins, as much as the already invisible virtual faith they put into the value of the dollar in all of their online transactions that are also digital virtual.
For now, since it's new, the paradigm is inevitably about cashing out bitcoin for dollars because dollars spend mainstream. This is the single area that is in people's way - the difficulty in escaping the bindings of the USD as the "end result" instead of a bad forced alternative.
But to consider faith in a currency, when people en masse would sooner trust pretend money and just trust the next guy one on one than trust USD currency that should be all you need to know to recognize the writing on the wall for fiat currency issued by governments and private banks. That's like saying Joe would sooner use Monopoly money than USD if Bob accepts Monopoly money in trade for goods and services.
So for now, absolutely, many people will put money into bitcoin and escalate their holdings, then cash out and buy stuff, probably the big stuff like cars and houses and whatnot, to shore up physical security but keep investing in bitcoin to also increase their shore of wealth...which is the ultimate security because eventually it will be mainstream and then the lights will flip on for people that they've got a security blanket and it's perfectly fine to jump off the sinking ship once and for all...and the more people who do that will tank the remaining value of the USD once and for all. It wouldn't wreck the economy though because of adoption and the number of people who are now trading and earning bitcoin.
Governments can ban it all they want but what they can't do is enforce it...once that is understood, people would be more ready to adopt it.
As for purchasing power of the dollar, 10 years ago I bought a bag of Tostitos, a jar of dip, some shirts and a 12pk of cokes and it cost about 30 bucks. I just did that today and it cost me 96 bucks at Target. All the way home I was having the epiphany - I should've just bought into bitcoin!!!