Will iMessages sent on an iPhone using Wi-Fi show up on the phone bill?

I use an iPhone and text other iPhones, iPods, and iPads on Wi-Fi using iMessage. Will these show up on the phone bill? Or are they separate, since they are sent on Wi-Fi? And when I don't send them on Wi-Fi, would those use up data/show up on the bill?

No they shouldn't its like an email, but if your messaging when not connected to Wi-Fi it will use data

Daniel nailed it.

No because imessages are not sms messages, so they will not show regardless of whether its celltower or Wi-Fi.

Nope. IMessages and SMS are different. IMessages are free and unlimited. SMS are text messages that use up your texts if you don't have an unlimited package. The only thing that iMessage will cost you, is your data package, but just text (not photos) will probably only be a couple MBs or so.

Tip: If the text boxes are blue, they are iMessages and don't cost anything. If they are green, they are SMS and are using up your text package.