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.
Also, according to the FARs and the 7110.65, a VFR and IFR aircraft are equal, neither have precedence over the other. The only time an IFR aircraft would have precedence would be if a Special VFR aircraft was present in the airspace.