Yes, the Morsi overthrow is a coup as, by the definition of the word, a coup is an overthrow of a previous regime. Those some definitions of the word "coup" list it as a sudden and surprise overtaking, this need not be the case. Other definitions list it as any overthrowing at all.
Whenever a political leader heads into murky waters based of accusations people always believe it is the media or some form of coup trying to take over and conquer whatever that leader is in charge of. I think they have every right to overthrow him since it is there government, and if he is guilty for what they are charging him for he deserves to be treated just as everyone else. It is their government and if they want to overthrow someone they should have right to do as they please since it affects their daily lives.