But will it be cheaper or more expensive than using a credit card?
Accepting Bitcoins is surprisingly expensive. There's a volatility risk, and for a currency that can change by 10% in minutes, that's a real problem. Coinbase (which is a dealer, rather than an exchange) has a posted buying price, good for one minute, and some shopping cart systems use that. But that price is usually lower than the prices on the major exchanges; there's a conversion cost. So, as with retail money-changers, you pay a conversion fee. Also, like most money-changers, Coinbase will briefly stop buying during periods of high volatility or if they have trouble unloading their Bitcoins.
Then, of course, there's prying the money out of the Bitcoin broker or exchange. Overstock is probably in a strong enough position to demand a daily sweep into a real bank account, with serious penalties for failure to deliver.
If you look at the few Bitcoin-accepting businesses that sell real products with typical mail order retail markups, the Bitcoin price is usually significantly higher than the US$ price. Most of the stores that currently accept Bitcoin are selling T-shirts, posters, remaindered goods, and similar crap. Of course, that's what Overstock does, so it may be a good fit.