If I change my network interface card on my MacBook Air 2013, which I assume to be my AirPort/Bluetooth card, will it change my laptop's MAC Address?
Yes, that is correct; it will change.
Your MAC (Media Access Control) address is assigned to network interfaces, not to the computer. For example, on this WiFi adapter from a Macbook Pro, you can see the MAC address imprinted on the chip (circled in red)
You can even lookup the manufacturer of the WiFi adapter by entering the first six characters into a lookup tool like this one. In this case, "58b035" comes back as "Apple, Inc"