No. Cancelling any Apple managed/billed subscription does not provide a refund, but just cancels the automatic billing at the end of that billing cycle. That being said, if you are unhappy about the subscription you paid for previously, you can request a refund by calling 800-MY-APPLE and ask to talk to the iTunes department. In my experience, they most often will credit you for a software app purchase, or a song or a subscription's past month.
Note: if you reverse a charge from your bank, that can lead to more problems and actually ban you from using that card again at Apple. It also can lock up your Apple ID account.