If an online business accepted credit cards without collecting security information, would increased sales outweigh the added fraud losses?

Not really. It is highly dependent on the vertical you are in and what you are selling. The onus of fraud and chargebacks on a merchant can be pretty heavy and time consuming. Gaming server access sales for example have a much higher fraud percentage than say a site selling fonts. Physical vs Digital makes a big difference as well. In the physical world when a fraud happens, there are tangible costs to pay, with the digital world the hurt is much less.

Many companies will take basic information (Name, Card Number, Exp, CVV) to process, but nowadays, such companies have information on file about you (take Facebook Credits for example). If you use a card there, minimal information is required, that's because (a) Facebook knows who you and your friends are (b) Digital sales, less hurt.

It all honestly depends what you're selling and how high the fraud rate in that vertical is. How you find your balance between security and customers who are agitated by providing too much information, is a balance you will learn yourself.