Yes, if you paper
file (mail in)
your Federal return you will have to mail
in your State return as well (it can't be e-filed
without a Federal e-filed return).
State filing - You will want to file an extension for your State until you receive your ITIN. This is because the application for your ITIN is a Federal filing. Most States will not process your return without either a SSN or an ITIN. (However some states will accept state filings with W-7 attachments. Please contact Iowa (IA) State (click the blue link) for more information and ask if your State will accept a State tax return with a Form W-7 attached).
When the IRS assigns you an ITIN, update your returns (both Federal and State) in TurboTax with this new information and then you should be able to e-file your State return. Many States give an automatic extension when you file the Federal extension Form 4868, just file a federal extension even if you don't think you will need it for your federal tax return. But check with your state's Department of Revenue to make sure that your state doesn't have a separate state extension filing.