I think to try (at a very soft volume) is OK. If you're not getting by the first time through, DON'T keep plunking and throw the singer off. I find that to be annoying and rude. I think, "I wish they would stop because it's messing with the spirit."
Your scenario has happened to me, though I've been playing a long, long time. BUT, I haven't always played in church and don't know many songs. Instead, I sit there and devote my attention to the singer, praising the Lord and encouraging the vocalist with an Amen, a hand clap or a wave. I'm not going to sit there looking like a deer caught in head lights just because I don't know the song. And worse, sitting there looking remorseful or stupid. I'm not going to let my frustration show to the people. God knows my heart. Now, people that may criticize, "Dang, she can't play that" are the ones that can't even play Mary Had A Little Lamb. I have a very high regard for singers because I was raised by a great singer. At any cost, I don't disrupt the singer.
Then, when that's all over, I go home and look the song up or try to find a recording of it, or find it in a hymnal.
Did you learn these songs yet? I always say if you know a few of them, you can play most of them.
Love,
Lisa