The green brittlestar is a KNOWN PREDATOR IN THE WILD.
If this is what you have, then absolutely. I have never had an issue with my 3- that is meaningless. It is a known fact that they can do this. It is a scientific observation and publication.
Other species...eh, not so much.
What color, how big, and what do you feed it?
That being said, lawnmower blennies can starve to death. Also, if it was a new fish it is at high risk of death. So we need more information. YES, it is possible...NO it is not a sure thing.
I would propose that more fish die and are consumed rather than being killed. We just like to believe they are killed. the answer to your question is we may never know.