No.  It's a flat fee per version.  And state is extra.  The fees are to prepare the return whether you efile or print and mail.  But if you want to have the fees taken out of a federal refund there is an EXTRA 34.99 Refund Processing Service charge for that.  So try to use a credit card and avoid the extra fee.

Oh, and the fees usually go up during tax season.  The fee is determined at the time you file or want to print.  So you can pay early to lock in a current price.  You can see the current Online fees here,

https://turbotax.intuit.com/personal-taxes/online/