Can I use TT online with my purchased CD?

No, they are 2 separate products.   You could get a refund for the CD if you don't want it then use Online TurboTax.

Why would you want to do that?   If you are used to the desktop version, you may not like Online TurboTax as much, and there are some limitations to the online product.

The CD version is a better product.  It can prepare multiple Federal returns with up to 5 Federal efiles, while Online TurboTax can only prepare 1 Federal return per account per year.

In Online TurboTax, a state return preparation is an extra 44.99.  

Depending on the edition, several desktop editions have a state program included.  Basic Edition does not have a state program.  Desktop Deluxe comes in 2 versions--one that is Federal-only, and one that is a combo Fed and State.  There is a 24.99 to efile a state return (no fee for New York), but no fee to print and mail the state returns.

In Online TurboTax, some editions have form limitations, while in desktop editions, there are no form limitations.  The CD version can prepare all the usual Federal forms.    Desktop Basic cannot import from ItsDeductible.

The CD version has the popular Forms Mode for direct viewing, printing, even editing of forms during preparation.  Online TurboTax does not have that feature.