Just Changed to Tmobile. Sim Card Not from Verizon Message.

Yes it continues to work.
If I restart my phone it may come back.
Now, when I open my home page and if there is a message that I have a non verizon sim card, press and hold down the message until it turns black and there is an "I" to the far right of the message.
Press on the "I" and the app window will pop up. Click on Force stop of that app and the message will go away.

Good luck!