Qi is Qi and has nothing to do with Lightning ports. Different question.
The answer to your real first question, "If you buy a QI charger and get a new iPhone will CarPlay work through the QI Charger?", depends on whether your car (or aftermarket head unit) supports wireless CarPlay. Some do -- BMW does, I think -- but some, like my Honda, don't.
Putting a Qi pad in my car will let the phone charge, and it'll still do the same basic Bluetooth functions as before, but I'd lose out on CarPlay. I'd much rather retain CarPlay than add wireless charging.