No -- You can't scan the composite 1099 into TurboTax.
However, what you can do is enter a summary of each category of transaction (short-term with basis reported to IRS, short-term basis not reported, etc.) You can then mail in the detailed statement to the IRS along with Form 8453 as a transmittal document. TurboTax will walk you through the process.
Please see this TurboTax Help article for instructions: How do I enter a large number of stock transactions in TurboTax Online?
[The steps are similar in the CD/Download version of TurboTax.]
