Dunno, the BBE is a "magic box"

It may have boost capabilities too, dunno, never used one. Some like what BBE does, others don't. I have never used one with a guitar, I guess I'm too much of a purist. With a whole mix, sometimes I like it at first, but after a while, to my ears it can sound artificial in a way that I can't quite describe. YMMV
There is no reason though, that you can't have 2 FnC's on yer board - one on all the time, the other set as a dedicated solo boost. I use mine for a boost, and tweak the eq sliders just a bit - for a LP type guitar using the neck pickup, I will bring the 200 hz and maybe the 400 down just a bit so its less muddy. For a strat, I might go the other way to fatten up the tone for a solo, especially for the bridge pickup.
That's why I like an eq for a clean boost.