Some groups favor more than others. Example, Switchfoot - Meant to Live. Bassist is using a fuzz, Reverb, and some other effect for the intro, and then a light overdrive (sounds like an OBD-3) for the chorus.
There are other times where the effects won't be so obvious but the bassist will be filling in other areas such as ambient swells ala hillsong and Jesus Culture. I recommend checking out their videos on their respective rigs. JC bassist breaks down more for what and how he uses each pedal (Like having a TCE Nova ND-1 to use on 3 songs in conjunction with his volume Pedal to do ambient swells).
I would just say don't dismiss effects pedals completely. You don't need effect pedals to worship. However, the added intricacy and diversity of sound Is akin to choosing to paint with a palette that bares more than just primary colors. You don't need the extra colors, but the diversity and complexity they offer make for deeper self-expression. Our expression of worship through our instrument is an expression of what's in our hearts for God.
Psalm 33:3 Play skillfully and with a loud noise.
Even better is when we present what we want to do to the Holy Spirit and let our Father direct how our sound should go, whether or not He wants overdrive or a simple clean tone because after all this is for Him.
I've seen first hand how God can influence effects and sound.