It is possible to install other OSs in the Edison, but the supported and official OS is the Yocto found in the Software download section https://communities.intel.com/docs/DOC-23242 . You can try installing it and post your results in the community.
I will probably try to install from sources to see how it goes. I thought maybe someone had already done it, as part of the 21st century robot project...
Which I will be per-purchasing soon.
Could be a bit challenging as step one for building from source is:
sudo apt-get install python-rosdep python-rosinstall-generator python-wstool python-rosinstall build-essential
don't have sudo installed nor apt-get... but trying opkg instead, I don't see any of the python items above in the repos, including AlexTs...
I'm also looking to get ros for edison.
I have found that bmwcarit had made a yocto layer for ros (hydro) :
I have successfully built the ros ipk with this layer.
I now need to test them with edison. I will make a tutorial soon.
... logging to /home/root/.ros/log/db7ee528-7181-11e4-bbb8-de8966996b16/roslaunch-edison-257.log
Checking log directory for disk usage. This may take awhile.
Press Ctrl-C to interrupt
Done checking log file disk usage. Usage is <1GB.
started roslaunch server http://edison:32990/
ros_comm version 1.10.11
auto-starting new master
process[master]: started with pid 
setting /run_id to db7ee528-7181-11e4-bbb8-de8966996b16
process[rosout-1]: started with pid 
started core service [/rosout]
cat > /etc/opkg/base-feeds.conf << EOM
src/gz all http://yocto.simkim.net/deploy/ipk/all
src/gz edison http://yocto.simkim.net/deploy/ipk/edison
src/gz core2-32 http://yocto.simkim.net/deploy/ipk/core2-32
opkg install roslaunch
then follow (from On the Linux system, ensure that the own host's name in resolved by adding) https://github.com/bmwcarit/meta-ros#usage
I will take a look soon. Some of the difficulties starting out on some of the instructions start off with doing things like:
sudo apt-get install xxxx
But sudo and apt are not in the default installs. Luckily we can now install them from AlexT_Intel repository, but some of us may need additional instructions on how to then configure the apt system to work...
I am not sure how much of the above instructions are done on a PC and how much is done on the Edison. In my first attempts at building ROS from sources on the Edison, when I got up to the places that did things like bitbake, internal to those systems were calls off to apt-get (I believe with sudo). I believe that apt-get was not 100% hard coded, but instead depended on which OS it thinks it is running on. If I remember correctly it did use a different package manager for a few of them.
So at the time was not sure if the best approach would be to try to figure out how to install apt (which you have done) and know how to configure it, or see if we could have it somehow detect the yocto and use opkg instead.