No. While the emergency alert may look like a text message it is not a text message.
Emergency alerts are sent via Cell Broadcast distribution. Cell Broadcast is a mobile technology that allows messages to be broadcast to all compatible wireless devices within a designated geographical area. Cell Broadcast is designed for simultaneous message delivery to multiple users in a specified area, and is not affected by network congestion because it uses a dedicated part of the network, separate from that used for traditional voice and data traffic.
Cell Broadcast can be compared to radio broadcast. Radio towers broadcast music to people in defined geographic areas as long as the individuals can pick-up the broadcast signal and have their radios turned on. Cell Broadcast messages similarly are delivered to those compatible wireless devices that are within range of cell towers and antennas in the designated area. Location services do not have to be enabled on your wireless device to be able to receive alerts.