Not really.
I had no choice in paying my taxes on it at the time I earned it. It is post-tax money. Right now, I have the choice to take it out and spend it or keep it saved.
Right now, if I take out post-tax money and spend it, all I pay is a sales tax (which I would have to spend anyway).
Talking about freedom and choice is obfuscation - the fact is that money I earned in the past was already taxed as income. Now it would be taxed again by the same sovereign under its plan to give us an alternative to income tax. That's taxing the same money, twice.
New interest my money earns in the bank is another matter entirely and in that case you are right.
There is no obfuscation except, perhaps, in your understanding of the present taxing mechanism. If under the present tax you took the money and purchased things you would actually be paying a sizeable amount in hidden (or cascaded or embedded) taxes and other costs (such as compliance costs) that increase the price of everything.
These have been found by some economists to amount to from 20 to 25% of the price of things. So you'd be "paying a tax", in effect even now by having these higher prices. And that would be the case no matter what you purchase.
With the FairTax, not only could you keep the money earning as an untaxed investment, but if you chose to spend it you'd have the choice to either buy taxable of untaxed items, depending on what was purchased. With the present system there is no such option and any income from investments would be taxed.
You'd actually be better off under the FairTax it seems to me.