Can you deburr copper pipes with a fitting brush?
The fitting brush will work if you use it with the proper sized copper pipes. When I say it will work I refer to cleaning oxidation off pipe and fittings. You should expect reasonable results for both the outside of the pipe using the holes in the tool and for inside of fittings using the brush. 

This brush will not work well for removing burrs on the end of cut pipe. For that you need some type of reamer tool for the inside of the pipe and a file for the outside edges if you are cutting with a saw (a rotary pipe cutter will not leave a burr on the outside that would be of any note). 

In the end, sans the tools of various types, there is still emery paper to clean up pipes and fittings too. Steel wool works too but may leave more debris inside pipes and fittings.