If it’s text via Wi-Fi while your phone is on airplane mode, yes.
If it’s SMS, no.

Lots of flights offer onboard Wi-Fi these days (some with an extra fee), and if your phone allows you to connect to Wi-Fi even in airplane mode (most phones these days do), then text or chat all you want.

The reason texting or any cellular communication is banned on flights is because it relies on cell towers and your phone is constantly transmitting strong signals and trying to connect to cell towers – so does your airplane. The signals your phone sends out can interfere with your flight captain’s communication with the control towers.

Aside from safety, not putting your phone on airplane mode won’t do you any good. Since you’re constantly moving in high altitudes, you’re always going to be far from the cell towers your phone relies on for texting. Your phone will try hard to connect to those cell towers and drain your battery but will never get a steady signal because you’re constantly moving from one cell tower to another.