FB Messenger Security
Yes, it is secure.  The connection is made using TLS 1.2.  This is from a tcpdump capture on my device:

192.168.0.11  31.13.69.195 (edge-mqtt-shv-01-iad3.facebook.com)  TLSv1.2  Application Data
31.13.69.195  192.168.0.11                                       TLSv1.2  Application Data