Does emailing on a verizon phone cost extra?

I have an alltel phone and when we used to be with alltel when i sent an email from the phone it would connect to the internet, or try since i had data locked on my phone because i dont have a data plan, it would show a message that said data is now locked every time i tried to send a email, now that i updated and alltel was taken over by verizon i still have data blocked on my fone but when i send an email it doesnt show the message anymore i have free texting, i have an LG Banter, so does it cost extra when i email from my phone?