No, this is a serious customs violation. Complete vehicles (HS Code 8703) and auto parts (HS Code 8708, etc.) are subject to completely different import tax rates. Combining them on one invoice could lead to the invoice being returned by customs and may expose you to tax fraud accusations at the destination port.

We will directly check the registration certificate (the big green book) and count the number of changes.

Absolutely. Even if you clear customs through gray channels, local commercial insurance companies will refuse to cover third-party liability insurance due to the vehicle not complying with national traffic laws; additionally, the vehicle will definitely fail the annual safety inspection at the local DMV.