Yes. CYPD3123 still function if cannot talk to CYPD2122. With original Cypress reference design CCG3 CYPD3123 is communication with CYPD2122 via I2C+INT. Which is means the CYPD3123 is working as I2C master bridge to read and write register of CYPD2122. So, I could recommend you make below customize in CYPD3123 firmware to remove I2C master bridge.
1. Disable HPI (I2C master) + INT. (Option)
2. Remove CTD funcitons.
#define DISABLE_CTD_US (1u)
//#define APP_I2CM_BRIDGE_ENABLE (1u)
3. Example project for your reference. https://community.cypress.com/community/usb/ez-pd-type-c-usb/blog/2018/08/23/ccg3-drp-porting-from-ctd-us