Will the IRS find out that I had paid the State its due by check, and that I should get a full refund amount from my Federal Tax Refund instead?
There is no "retired" status and nothing about retired goes on a tax return at all. (If you mean you entered your occupations as retired, then that is only for statistical purposes and you can put anything there - it is meaningless.)
The IRS is paying no attention whatsoever to your state return and does not know if you owed the state or if you paid the state. Your state tax due can NEVER be paid from a federal refund.
And as stated, "retired" is not a filing status. Your choices for a filing status were Single, Married Filing Jointly, Married Filing Separately, Head of Household or Qualifying Widow(er).
Good thing you paid the state tax due! Many people misunderstood that part. The state tax can not be deducted from the federal refund. Never. You can only have the Turbo Tax fees deducted. You will still get the full federal refund minus any fees you had deducted plus the extra 39.99 Refund Processing Service charge (44.99 in California).
Turbo Tax just shows you a screen at the end showing the Net amount of federal and state combined. But it is just for your own info. You do still have to pay the state yourself separately. See,
Check the printout or PDF of your return; look for the state cover sheet with the Turbotax logo. If you owed tax, it will show the payment information and how/when you decided to pay. Read the state payment instructions carefully since most states cannot be paid from within the TT system and requires additional steps.