f the rate of GST on the supply on which TDS is applicable is 18% and TDS @ 1% is made at the time of payment, will the effective rate of tax become 19%

No, tax deducted at source by the deductor is available to deductee as credit.
Therefore, the deductee will effectively pay tax at only 18% (17% by cash/input tax credit and 1% by utilization of TDS credit).

(ICAI FAQ PUBLICATIONS 06-09-2017 TAX PAYMENTS, INTEREST, PENALTY AND OTHER AMOUNTS:FAQ NO. 45)