Texts shouldn't be a problem as long as you have a mobile signal (no data required), but MMS require a valid MOBILE data connection to work, unless your carrier supports WiFi Calling or has a WiFi-enabled texting app (like Verizon's Messages+). If you're in Airplane mode and just have WiFi, then texts wouldn't work at all (unless the aforementioned WiFi-Calling conditions are supported by your carrier and network)