Actually, no. This is a common misconception.
If someone calls you while you’re driving, let them leave a voicemail for heaven’s sake. The idea seems to be that if someone calls your cell phone and you don’t answer it immediately, the world will come to an end or something. Trust me, it doesn’t. Lots of times I’ve called people back and said, “Sorry I couldn’t take your call, I was driving.” They still get to talk to me a lot sooner than if they called my home, and I don’t endanger anyone’s life.
Back a little closer to the sbject of this thread, it is certainly possible for the mobile carrier, when your phone is on, to download new software to your phone without your knowledge. This software could include operating software that could affect (probably the next time you turn your phone off and on) how, say, the power button works, so that you would think your phone was off, when it simply did not process calls. But remote activation of the microphone would still be possible.
I have no idea whether anyone ever does this, and of course they would have to know ahead of time that they wanted to use the phone for a listening device (they couldn’t just do it on the spur of the moment). But certainly it would be technically possible to set it up. It would take a fair bit of programming, because they’d basically have to alter the OS of the phone, and they would probably have to do it specifically for the particular phone model. And of course, they would have to either hack the mobile company’s systems or (if they are law enforcement) get the cooperation of the mobile company (although most employees of the mobile company would not know about it). So I’m not saying how simple or even how likely it would be, just that it is technically possible.
And I’m really glad I don’t live where the people can’t leave a phone hidden in a car in a church parking lot for 10-15 minutes to go to confession without having to worry about it being stolen. Although you might have to worry about it melting in the summer.

Perhaps the phone could be left in the pew, in the rack or shelf where the missals/missalettes/hymnals are?
–Jen