Does the prostration of forgetfulness (sujood as-sahw) become obligatory if one inadvertently recites the salutation upon the Prophet (peace be upon him) in the first tashahhud?

Invoking blessings upon the Prophet (peace be upon him) in the first tashahhud is legislated according to some scholars. However, the majority of them are of the opinion that it is not legislated. Nevertheless, it does not necessitate the prostration of forgetfulness (sujud as-sahw), so the prayer is valid, and the prostration of forgetfulness is not required.