What happens if a change the SIM card to my phone? Will Android add the contacts of the new SIM card to my Google Account?
What else could happen?
You'd probably have a different phone number, and possibly a different contract/data plan for your device. If your device is SIM-locked, you might have no service at all (i.e. no calls, SMS, internet) if the SIM card is from the "wrong" provider.

Apart of that, nothing would happen: contacts on the SIM card are not synchronized with any account.