Very unlikely. A canvas is technically just a two-dimensional array of pixels. When you draw a blue rectangle to the canvas, you just change the color values of the pixels which were there before. The old color values of the affected pixels are lost. The information that these now-blue pixels belong to a rectangle object isn't save either. They are just color values with no special relation to each other.
It seems this has not been discussed a lot on programmers.SE but on stack exchange you can find a lot practical tools and methods to perform this task.
Generally Google Chrome is a good tool for it but off-course it is not cross browser. So, if performance in other browsers should be as good take a look on the specific tools for those browsers (look for profiler / performance profiler / etc).