While it might be theoretically possible, I don't think it's possible in practice. A business has expenses which must be paid in dollars (or whatever the real-world currency of their country of operation is): wages, sales tax, insurance premiums, utilities, interests on loans, postage, custom duties and so on. Without a way to convert bitcoins to dollars, they won't be able to cover their expenses.
Now, granted, they could do a mix economy, selling in both dollars and bitcoins, using their dollar sales to cover "hard currency expenses" and using their bitcoins sales to buy services and goods available in bitcoins. The trouble is, it's not going to be worth it, because you can't use a surplus of bitcoins for anything. You can't pay it out in wages, you can't invest it in another company, you can't use it to pay dividends; in short you can't use it to make more dollars (or even to make more bitcoins). Your business is still dollar-driven: it's your income in dollar that determines how well your business is doing and whether you will swim or sink.
Basically, every single sale you do in bitcoins carries with it a massive opportunity cost. Where the income from a sale in dollars can be used for anything you want or need, an income of bitcoins can only be used for buying whatever goods and services a) you require and b) are available for sale in bitcoins.
Now, while it's true that it's sometimes worth taking an opportunity cost in order to expand into a new market, that's not the case in this situation. Your business is dollar-driven, so you can't expand without an increase in dollar income. An increase in bitcoins income is just going to make you accrue bitcoins in excess of what you can use.