ATC would only deny a request to transition through Class B airspace if they have a reason to justify it. They can't deny a VFR aircraft's request to transition the airspace for no reason.As long as you're able to fly through it (hold a private pilot's license or a student pilot's license with the appropriate sign off), your request will likely be granted, but then, yes, you'll have to follow all instructions whether or not you like the instruction.
I have to say, at least at Dulles (which is a lot less busy than O'Hare but still quite busy) you're not going to get a bravo clearance in the middle of an arrival or a departure bank unless your a lifeguard helicopter or some such. There are simply too many airplanes flying every which way to allow VFRs to start wandering in. In Chicago there's no SFRA, so you can just maintain VFR outside of the bravo without talking with anyone, but I would be very surprised if they rerouted you as an IFR away from the airport, only to allow you into the bravo VFR.