It is perfectly possible to control this arm with ROS, it won't be the most smooth or precise arm in the world but I'm guessing that's what you expected anyway!
In order for any robot arm to be controlled by ROS (MoveIt within ROS most likely) there needs to be a hardware interface that can tell ROS the positions of each of its joints and also control the position of the joints so they follow a given trajectory over time. The arm you linked to can do the second half of this if you were to modify the firmware so it was ROS compatible, however the servos it's using don't have any position feedback they're open loop. In this case you can assume that the arm is in the position the servos are being commanded to go to, this is an assumption but should be find for a toy robot like this.
If you're not familiar with MoveIt I recommend having a look at the documentation here and working through the first few tutorials. Once you're confident working with simulated robots, then you could start planning integrating this new hardware.
Hope this helps.
