Would it be possible to implement ROS with a robotic teaching arm?

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"Implementing ROS" with an arm sounds a bit misleading I think. ROS is already implemented (but of course evolving over time). You can certainly use a multitude of ROS tools with hobbyist hardware though. If you create a URDF model, you could easily visualize a robot model in rviz or even plan motions using MoveIt!. Some caveats apply of course, for example if your arm doesn´t have joint angle sensing, you could provide fake joint angle measurements by just taking the desired values you sent to the system (which might or might not work very well). You´d likely also have to do some low level interfacing with a Microcontroller, but rosserial_arduino, ros_arduino_bridge, rosc and others could help with that.