Yes,
He blots people out who die having rejected him
He who believes is not condemned, He who does not believe is condemned already
they wre not of us because they were in a condemned state and they remained in that state. They were never born again
I do not hold that all men are in His Book of Life, but, even if you wanted to assert that, He differentiates between Church members in Sardis, all of whom had been washed, but some of whom had soiled their garments, and some of whom had kept them White, and the latter would
not be blotted out of the Lamb's Book of Life, but would be confessed before the Father, meaning that the former, by contrast,
would be blotted out (and if the men were unsaved, and you get blotted out for sinning, surely they would have been blotted out long before the writing of the letter), and would be
denied before the Father and His angels, because whoever denies Christ before men will be denied before the Father, and "they claim to know God but in their works they deny Him", so they denied Christ in their works (soiled their garments), and so would be blotted out, as God said before "the ones who have sinned against Me I will blot out of My book" (Ex 32:33).