Theoretically it is possible but it requires you port everything to the Intel® Edison platform on your own since there is no documentation on how to do it and it could be a long process. I suggest you to use the Yocto image which is the one we support in here. But if you are looking for other alternatives you can check ubilinux which is based on Debian “Wheezy”. You can get the latest Yocto image in here and more information on ubilinux can be found in here. The ubilinux image is supported in the Emutexlabs forum. I hope you find this information helpful.
One advantage of Edison is that it is an x86 architecture, your software will likely compiles on it. Finding the correct binary package for yocto may be not as easy as ubuntu.
Looking briefly here, it has python and numpy here: http://repo.opkg.net/edison/repo/core2-32/