Looks like only if you bought the Turbo Tax Desktop program from Amazon. Be sure to update your program. The link to buy Quicken just got fixed.
See this thread
TurboTax is not associated with Quicken - totally different companies.
If you mean the Quicken Starter offer that is an exclusive AMAZON offer when you purchase TurboTax from Amazon, then after installing and starting TurboTax the offer is at the bottom of the first screen.