No reason it shouldn’t. Kickr Core has all the standard Bluetooth and Ant+ protocols so it can be controlled by TR, Zwift, Rouvy, or any other app / program.
However, if it only comes with the Zwift Cog and not a full cassette, then you can only use erg mode if you’re only using TR. Resistance mode in TR requires you to shift and / or adjust cadence to meet the power targets.
Lots of good info on how to run TR and Zwift simultaneously at the links below.