Depends on the band, and the type of screaming.
On one hand, we have the Dani Filth style evidenced below
In that one, he never sings normally, and I thought for years that was just Dani's voice. However with the way the band is, I honestly could not imagine any other type of singing for their music, it would be like replacing Peter Steele, or Lemmy Kilmister
Then we have the newer version, the sing and scream, evidenced by Adam Gontier. This one seems to be more popular, and in some songs serves to draw more attention to specific lyrics in the song, which I think is the purpose of it. I like it because it keeps the song fresh
I don't know if Adam ever actually learned how to sing, since he seems to go from that sing-speaking that categorizes shitty musicals into his all-out rage scream