Oh, absolutely - this would be if I didn't want a straight-up clean boost but wanted to mis-bias the added gain stage for effect. For instance, there's a fuzz called the Baron Samedi which tacks a transistor-based boost at the end of a Bosstone, and by changing that third transistor's bias you can get some very interesting sounds.
I'm not certain this can be done with an IC, but would love to know!