No, not if you want to have the interest on that portion of the debt deductible. According to the IRS, the refinance would have to have been done within 90 days of the completion of the work to qualify as home acquisition debt.
Of course, you may still use your refinance to pay off your personal loan even if it is not within that 90-day window. However, it is treated as home equity debt, which is currently not deductible. TurboTax will calculate the deductible and non-deductible portions of your mortgage when you enter the information.