When browsing my "MyVerizon" call/text logs I noticed that whole conversations that were held via IMessage were omitted from the log. While conversations on my other iPhone that were IMessages from same iPhone/sender/number/etc... DO show up. Any idea what would cause this? Would sending IMessages to the email/Apple ID address rather then the cell # accomplish this?
iMessages don't go through your cell phone provider so they don't necessarily know about them. iMessages go through your network connection so to your provider they look just like any other network/internet/browser traffic.
If your text messages were from Apple device to Apple device (using iMessage for both sides), it's not going to show up on the provider logs.
If your text messages were from your iPhone (or other Apple device) to a non-apple device or an Apple device without a network connection but still connected to the cell network, that does go through your cell provider. They will have a log of those messages. You can tell which ones those are because the chat bubble on the Apple device is green instead of blue.