Yes, you could. And when you get it all back as a refund in 2017, you'll then have to claim it as income on your 2017 tax return.
You deduct the state taxes paid in 2016 on your federal return, which is prepared first since states need to know the federal AGI to prepare their own forms. Then, having deducted the state taxes, if you subsequently get a state refund (in 2017, since that's when you're preparing the 2016 return), that amount will be taxable income next year (with certain limitations).
So there's always a 1-year time lag, and it continues forever as long as you're deducting the state taxes paid.