No.
You may make a normal Roth contribution in addition any conversions you make in the same year, regardless of the amount of the conversion.
Conversions and contribution are two different things. Conversions do not count as contributions for the $5500 ($6500 for age 50+) contribution limit*.
*But, any contributions you made to a traditional IRA (TIRA) contribution, in the same, year, whether deductible or non deductible, do count toward that $5500 limit.
