No, although it could work there was another killer though read below. On some site ages ago I was reading a theory that the other detective was a killer, I will post the link if I find it.

Spoiler Alert(I can't find spoiler tags like IMDb used to have so stop reading)

If you listen to the commentary on the DVD you will hear Wes Craven mention that Angelina Tyler was the second killer. They filmed it but deleted it. I was to be revealed that Angelina Tyler's real name was Angie Crick and that she used to be in Sidney's English class at high school. She would also be revealed to be Roman Bridger's boyfriend. The scene where Gale and Jennifer Jolie look over the staircase and see Angelina getting stabbed would still be there obviously she never got stabbed and the pair faked it just like Roman tricked gale in the coffin.

If this ending had happened it would also have implied that there were four killers in either Scream or Scream 2

Another ending considered:

In a 2009 interview, Matthew Lillard claimed that he had been contracted to reprise his role as the primary antagonist, having survived his apparent death in Scream (1996), orchestrating new Ghostface attacks from prison on high school students and ultimately targeting Sidney. Following the Columbine High School massacre shortly before production began, the script was scrapped and re-written without his character and this plot to avoid development of a film which associated violence and murder with a high school setting.

That would've been interesting. It feels like they kinda recycled it in four with you believing Judy was one of the killers and I kinda like it. Every other film had a duo and would explain some inconsistencies on how he can be in two places at once

That would be interesting indeed. Back then I suspected Angelina the most. I was even disappointed when Roman's indentity was revealed but now I think S3 has its charm. Everyone expected 2 killers but we got 1 plus he was the "original" killer