If Roth money is recharacterized to non-deductible Traditional IRA is it reported on the 8606 for that year?

Is the recharacterized amount added to the non-deductible IRA cost basis, so the carry-forward amount for the next year is increased by the amount of the recharacterization?

Since taxes were paid on the Roth money before contributions were made, and the recharacterization goes into non-deductible TIRA, should that help to increase the cost basis for Traditional IRA?