I don't think so...
How would they see it unless the shooter was holding the handgun/rifle anyway?
If someone was holding a gun and aiming it, I'd think someone would sure notice that - wihout being told by the police/media what caliber bullet was used in previous shootings.
Unfortuntely, reavealing the caliber of the bullet would also tell a copycat what caliber to use - if they said (for instance) it was a .223, and shootings start up somewhere else, how would the police know if it was the same shooter or a copycat?
Also what if they said (for instance) it was a .223 - would that mean that anyone who knew of someone who owned an AR-15 / Ruger Mini-14 should call them in to the police as a suspect? Should sales of the caliber ammo being used in the shootings be suspended?
I don't think there is any benefit to letting out the caliber of bullet being fired at this point.
If those good citizens heard the caliber used was .XX, and that mildly suspected relative or aquiantence is known to have a gun in that caliber, then they make the call, and possibly the case is solved.
Remember the Unibomber was not nabbed by super sleuth FBI agent (who were 180* off in their profiling). It was solved by his brother, who had suspected him for a long time, and dropped the dime after the "recognition" was made from his published writings.
The caliber being announced could do the same thing.