No.
Only works with the new K2 printer.
There will be an upgrade system for K1/Max!

There will be an upgrade kit for the Ender 3 v3 and all K1 models.
The product is already visible in the Creality Singapore shop and is expected to be available from 20 January:
https://crealitysg.com/products...
469 Sungapur dollars is currently approx. 313 CHF.
We'll have to wait until it's available here (and hopefully the price will drop a little).
The K2 Plus (with or without CFS) is also extremely expensive at the moment.

The CFS MULTICOLOR SYSTEM BOX from Creality is specifically designed for use with certain Creality 3D printers, but there is no specific indication that it is compatible with the K1 Max.

To ensure that the system is compatible with your printer, I recommend checking the official documentation and compatibility list from Creality or contacting the manufacturer directly.

If you need more information, you can also ask the Community for experiences with this combination.