No, it is not necessary to run Remove Report Cards/Transcripts/Statements from NetClassroom before publishing updated ones to NetClassroom.

If you are publishing report cards/transcripts/statements for the same group of students, Publishing Report Cards or Transcripts it will overwrite the previously published ones.

The Remove function is designed to remove report cards/transcripts from NetClassroom without replacing it with any other information. Both functions only affect the student(s) that you are including in the Filters tab of the parameter used with the process.