No.
That's the short answer--with the additional caveat: unless the organist is late and is holding things up.
During a frantic round of late day phone calls, at the end of what was a very long day, a friend of mine, whose daughter is studying organ, left me a quick message. "The announcer talked over my daughter's organ prelude this morning. Just thought you'd appreciate that."
This particular individual has been at the exhaust vent end of some of my rantings about this very subject, hence the zinger about my appreciation for this subject. There is, perhaps, no more efficient way of saying that the music doesn't matter than to talk over top of it--any part of it. For some reason, announcers think that what they have to say is so urgent that they can't wait for the organist to finish. In spite of the supposed importance of these announcements, they can never coordinate all this with the organist, either. All it takes is a little meeting, where it can be decided to play the prelude a bit earlier, or to take up some other similar adjustment. Alas, that takes forethought, and liturgical forethought--so it seems--is considered to be one of those ugly Protestant vices.
"Oh, clearly you organists are just a bunch of nutty megalomaniacs! Obviously, the prelude is not part of Mass, therefore we can treat it however we wish."
Well, the prelude surely isn't the same as the Gradual or the Offertory, but it does serve something of a purpose. It is, in a sense, the sonic version of the indirect path into the sanctuary. Some ancient cathedrals have several walls, which extend the transition from the secular world to the sacred. The walls create the space necessary to prepare to enter the church. The prelude acts in the same fashion, soothing the anxious mind and preparing our hearts for the liturgy. This sounds to me like a noble purpose.
A frustrated David Zinman once turned around in Baltimore's Meyerhoff Symphony Hall and declared that "silence is the canvas upon which a musician paints his picture." Indeed. I might add that everyone likes to feel appreciated and needed. There is no better way to demonstrate that to your parish organist than by staying out of his way and not treating his playing as background window dressing. I cannot speak for anyone else, but the kind of disrespect shown to my friend's daughter today gets to my last nerve a lot faster than the usual sacred music punching dummies.
Let us be silent when it is time to be silent.