The consequences are essentially nil and you can actually still do a "backdoor" Roth even if your household income is low enough that you could contribute to the Roth account directly.
Backdoor Roth just means you contribute to a traditional IRA and roll over to the Roth.
If you're above the cutoff for a traditional IRA contribution, you don't get a tax deduction for the contribution to the traditional IRA, but don't have to pay income tax on the rollover amount.
If you're below the cutoff for a traditional IRA contribution, you do get a tax deduction for the contribution to the traditional IRA, but do have to pay income tax on the rollover amount.
Normal Roth means you contribute directly to the Roth account and therefore still have to pay income tax on your contribution.
In all three scenarios your final income tax owed should be the same.