Can you upgrade an infotainment system to CarPlay in a car that doesn't offer it?

No. The Infotainment system update comes from the car dealership only. Nissan has no idea what they are saying.

There is no update from Apple for Car Play that one can apply. Any CarPlay updates are sent to the dealerships to be applied by them. And any system software update to support Car Play or even Android Auto has to be applied by the dealer.

The Siri Eyes Free feature works with Bluetooth when CarPlay is not available.

Use Siri in your car - Apple Support

It's entirely possible your particular Infotainment unit does not support Apple Car Play, or Nissan has no update path for it if it does. Unfortunately car dealers are woefully misinformed when it comes to support and software updates for CarPlay and Android Auto

As an example Hyundai does offer software updates for select 2017 models to enable Apple Car Play or Android Auto. https://owners.hyundaiusa.com/us/en/CarPlayLoggedOut.html

Nissan would need to do something similar.

Maybe.

Depends on the Infotainment system. Some car dealers offer updates for certain Infotainment systems to versions that support Car Play. Other infotainment systems may not support the update. It's down to the hardware and software installed.

Contact your car dealership and inquire about the option of updating your infotainment system to support CarPlay.