Yes, if you filed your return with TurboTax last year, and your children were listed as dependents, then when you pay to upgrade, that information (names, birthdates, social security numbers) would transfer over to your 2015 return.
For more information on transferring your prior year return in TurboTax Online please see the following TurboTax FAQ:
https://ttlc.intuit.com/replies/3301662
