The short answer to this questions is a fervent “no”. While a logo is an important and valuable representation of your brand, your brand encapsulates far more. Your brand is the image that represents your business or organization to the outside world. Your brand is how everyone else perceives your operation.
The easiest way to exemplify this is with a practical illustration. If I asked you to describe the Coca-Cola brand, you would probably have a difficult time even recalling a specific logo. However, elements such as a bright red color, a particular script font, words like “cool” and “refreshing” and images of Santa Clause or a polar bear holding an old glass bottle readily come to mind. Each of these elements can stand on its own to some extent or combine with other elements for greater effect in bringing to your mind the Coca-Cola brand. None of them necessarily has anything to do with a logo, although a good logo would incorporate some of these elements.
In essence your brand composes all of the elements that conjure up the projected image of your organization in the mind of the consumer. If your brand is well-designed and well-marketed, often one or two small elements used in concert with each other, such as the combination of a particular color with a specific font, will advertise your company through brand recognition. This is why developing and implementing a solid brand strategy is a critical component of success in a market economy.