Can I receive texts when I'm on airplane mode on my iphone?

If during airplane mode, someone texts me and I don't receive them, will they come through when I turn off my airplane mode or are they just gone.

They come through when you turn airplane mode off.

No sure can't. Airplane mode cuts off all signal, thered be no way to receive texts or calls

When Airplane mode is enabled, it cuts of ALL WIRELESS SIGNALS connecting to your phone, ESPECIALLY Cellular signals (as Wi-Fi & BlueTooth can be re-enabled while Airplane mode is enabled, but NOT cellular stuff).

Therefore, you will NOT be able to receive any calls, voicemails NOR any text (plain or picture messages) as a result. HOWEVER, iMessages (messages sent between iOS devices like iPhones, iPods, iPads & Macs) can be sent & received if your connected to a Wi-Fi network while Airplane Mode is engaged. These messages will appear in a light blue background (light green background denotes an actual text).

You will receive them as soon as you will turn off the airplane mood.

No only if AirPlane mode is off.