I mailed in my out of state tax forms in January, but have not received a confirmation that they have been received?

You do not get confirmations for mailed returns.  

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

Right, but when I log into TurboTax, should it say something other than - status: Printed?

No.   If you mailed your state return and you KNOW that you mailed it, that is what matters.  The software program does not know that you put your return in an envelope and took it to a mailbox.  It will never show any more than "printed" in your account.   TurboTax does not receive any information or feedback after a return is filed whether you e-file it or mail it in an envelope.  It is a good idea to use a mailing service like UPS, FedEx or certified mail when you mail a tax return so that you know for sure it was received.

Does your state site show anything for your return?