Sorry, but NO. You must arrange to pay each as separate actions, and a refund from one cannot be directed to pay the other
The tax systems are entirely separate. The IRS won't sit around waiting if SC delays, reduces, or eliminates your "supposed" SC refund for any reason . Neither tax system wants the extra paperwork nightmare that would be generated if that happened.
You could wait to pay federal until you get the state refund deposited. But actually the tax due was due back on April 15 so you are late and interest is accruing. So even after you pay you might get a bill for interest to the date they get your payment.