Do deleted iMessages show up on text message logs for Verizon?

I have an iPhone 4 but my parents are in charge of the account. My boyfriend just got the same phone so we can talk on iMessage. I need to know whether my parents will see if I were to delete my iMessages on the text message logs online. Please answer!

Yes it will. You could get textfree (in the App Store) it will give you a number and you can text for free.

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