NO, amending your return will not delay the original e-filing of your return.
Form 1098-e is used to report any student loan interest that you have paid for the year. Student loan interest is reported as an deduction to your income when calculating your adjusted gross income (AGI).Student loan interest can be deductible on federal tax returns, but receiving a 1098-E doesn't always mean you're eligible to take the deduction.
You should be able to tell if your eligible and if it makes a difference on your return once you decide to amend your return in TurboTax. You should wait until your original return is e-filed and accepted before completing the amendment.
The link below provides information on how to file an amendment using TurboTax. The forms are not quite ready yet, but you can take a look at the directions for 2015 to get an understanding of what will need to be done.