I am planning on sponsoring my wife. She is currently on a study permit from India here in Canada and I am a Canadian citizen. My question is, does my wife need to continue studying while our application is in progress.
An outland application does not provide any legal status in Canada. Thus, if your wife were to discontinue her studies, she would be breaking the terms of her study permit and would be in Canada illegally. She could apply to change the conditions of her stay and be a visitor in Canada instead, but there is no guarantee this will be approved.
If your spouse doesn't want to continue studying, she needs to apply to change her status to visitor. If she simply stops studying and doesn't change her status, her study permit will likely be cancelled, leaving her in Canada illegally.