Correct. However, you either have to take an entangled pair of particles (the two electrons) and then separate them by the distance over which you wish to communicate , or you must figure out that two particles already separated by distance are, in fact, entangled. You could only confirm this by communication by other means to verify it. Either way, you have to travel or communicate normally over that distance at least once.
So, to use this method to communicate with someone in the Andromeda Galaxy, you either have to send one of the electrons there (at Max speed less than the speed of light) or receive (or send) a signal at Max speed the speed of light from (or to) Andromeda confirming that you have an entangled pair. Either way, you are waiting at least 2 million years, before you can start to use your entangled communication device to instantaneously communicate with someone in the Andromeda Galaxy, given that it is 2 million light years away. Unless we learn how to fold space...