Overdrive/distortion is really hard to use in a worship setting for me. I think (but I'm totally pulling this out of my butt) it depends a great deal on the ensemble size and the sound guy. Maybe on what the guitars are doing. Like, it wouldn't work as well in a 3-piece worship band as it would in a 5-6, where the overdrive would be less noticeable and just help you sit in the mix better. I'm always blown away when I hear isolated bass tracks from popular recordings on Youtube, only to realize that they are distorted. I never knew that listening to them back in the day.
This is one of my favorites:
And this one still blows my mind. You have to skip ahead to about 1:30. The bass sounds so farty, but in the mix, it just sounds fat. It's crazy.