No. It is risky to convert first because if the plan does not accept the rollover or it does not get done for whatever reason, then the conversion will be mostly taxable due to the pro rata calculations of Form 8606. Therefore, the reverse rollover should be completed before converting the remaining IRA basis.
When doing the reverse rollover, funds do not come out of your IRA pro rata with basis. Only the pre tax balance is distributed from the IRA and the plan cannot accept more than your pre tax balance. Therefore, the rollover check should be for your total balance less your basis, which leaves the basis in your IRA. Then when the plan has accepted the rollover and it is deposited in the 401k, you can convert the remaining balance of your IRA to Roth tax free.
To be clear, you could convert your basis first and pay no tax but only if the 401k accepts the rollover. If they don’t you would pay tax on most of the conversion, so it is much safer to complete the 401k rollover first.