Short answer: there is nothing that says “no” to this in all cases.
You would need to check out each situation.
A more detailed answer:
In my experience, the congregation is in “music on the side” mode before the service begins.
There are also some situations where singing could work:
A pre-service concert series
One church where I’ve performed concerts designates one Sunday per month as their concert Sunday. The musician(s) play a half-hour program which is followed immediately by the service. The congregation arrives 1/2 hour before the usual service time expecting to listen to the music.
A sung pre-service concert would be wonderful!
Congregation expects to listen
At The Riverside Church in New York, the prelude occasionally consisted of Mozart sonatas for piano and violin. William Sloan Coffin, who was trained as a concert pianist, enjoyed teaming up with an accomplished violinist from the congregation. However, at Riverside, the congregation is accustomed to hearing great music played by organists at the top of their field. People come early, find a seat, remain quiet, and listen.
A singer would be comfortable in this situation.
Most of the time
My suggestion would be to include a singer after the service has begun. When the minister is at the front of the sanctuary and the call to worship or opening prayer has been spoken, people are more settled.
Why planning matters
Choir members at a nearby church (not mine) told me that when they sang an anthem as the prelude, nobody listened.
The text of a song or anthem is much more important than background music. We need to keep that in mind when deciding where to place sung music in the service.
People who write advice columns about party/dinner planning say that instrumental music works best when guests are talking. The prelude can be seen in the same way. The congregation is just arriving, and they want to greet one another. When they are talking, the text of a song is lost.