The short answer is no. However, student loan interest is an adjustment when calculating your AGI resulting in less money owed or bigger refund. But you may have determined if won't make enough of a difference to upgrade.
There is also The Turbo Tax Free File program which is free for federal and state. And has more forms than the Federal Free Edition, like Schedules A, B, C , D, E, F, EIC, H, K-1, SE, etc.
NOTE: You will have to setup a new account with a new username and new password or it will take you back to regular Turbo Tax. To access & determine if you are eligible, use the link below.
https://freefile.intuit.com/