Yes, I experimented with bleach by-passing a few years ago using Kodak Ektacolor Gold film, and processing through C-41 with a dip and dunk machine.
It was easy to skip the bleach tank.
As you can see, the bleach-skipped negs ( top ) are very dense so printing times were very long !
I've used it on occasion for gritty look high contrast but also for somewhat desaturated high key portraiture. Not much to elaborate on; just skip bleach and embrace the distorted color and gritty grain.
I've done bleach bypass with chromogenic B&W films for years; I shoot XP2 Super at EI 800 for that process. Even in color, it's fairly standard practice to reduce exposure to allow for the extra silver image density. With color still films, however, the filter layer isn't removed, so you get that overall "fog" effect that you have to scan or print through. I need to try it with color sometime soon (considered it for WPPD yesterday, but it was too bright out -- I had loaded ISO 400 and exposures were already in the 1-2 second range).