Congrats, that Conquest Classic is a great bike. Might be the perfect commuter. I'm no expert (I'm on my first brooks saddle), but I would think it would probably be okay. The problem may be that you'll find the seat very uncomfortable on a flat bar bike. If you're riding more upright the sprung brooks saddles are better. I'd worry that you'd be especially uncomfortable trying to break it in.

Now, if your flat bar bike is more aggressive so a lot of weight is on your hands you'd probably be fine with the B17.