Distortion is very common in contemporary gospel music, but not so's that you'd notice it. You have to be VERY tasteful with it, there are certain specific areas that it is called for. Very much in the way that a keyboard player would use synth horns-- in the right places they add a lot, but play the whole song on horns and it sounds bad!
Rather than try to explain where, I'm going to list some examples that come to mind. And yes DuBose is in there.
Kurt Carr - In the Sanctuary
Shekinah Glory - Praise Is What I Do
Kirk Franklin - Revolution
Israel & New Breed - Magnificent and Holy
New Direction - New Direction
Lamar Campbell - More Than Anything
TD Jakes - Your Majesty
Fred Hammond - Pages of Life II Intro (and elsewhere on the album)
Byron Cage - Prince of Praise (Intro & Magnify)
Fred Hammond - You Are My Daily Bread/Lord of the Harvest
John P Kee - Right Here
Kirk Franklin - Hosanna
Donald Lawrence - Never Seen the Righteous
Deitrick Haddon - Dont Let Me Fall
These are in no particular order other than what I thought of them. Note that almost always, when the guitar has distortion it is either playing a melody line, or note for note what the bass is playing.
Of course, all these examples are rehearsed bands playing for professional concerts or in the studio. If you are playing in church, I would use the same format if you have a choir or praise & worship team doing contemporary songs, and your band rehearses (so you can practice the breaks and such where you use distortion). The less rehearsed your band the more sparingly I would use it, of course if your band is really good you may be able to flow together very well without rehearsal in which case you can be create.
Old school gospel doesnt often use distortion, however you can use an overdrive on your guitar to get a more bluesy sound.
Contemporary Christian Praise & Worship, and Christian Rock, may use a lot of distortion on chords for rhythm parts. But that's because the music is more guitar based and the guitar doesnt interfere with the vocals as much.
