Originally Posted by
javabytes
True, it could, though that would require not just connecting to the Wifi network but also buying internet access, which it seems OP did not do.
With US T-Mobile users on Delta, in-flight WiFi was at times freely connecting for communication connectivity if having used it repeatedly before. Even if never having paid for DL WiFi.
But in this case the OP may have had one bar of cellular service for long enough to get an SMS.