USB charging ports are supplementary to basic USB 2.0 specifications. In official (USB "sponsored") Battery Charging Specifications (BC1.2) the advertising of port power capabilities occurs BEFORE any connect event occurs, so the levels of initial BC1.2 handshake are chosen to be BELOW normal initial USB signaling levels, such that the USB part of front-end transceiver won't be confused. After the BC1.2 protocol completes and VBUS capability is communicated to device, the D+/D- lines are free from the "charging signature", and can operate in accord with standard USB protocol. This is how the "CDP", Charging Downstream Port is defined, the advertising handshake happens, and then it is gone.
I am not aware of any definition of "CDP" (host data ports) with proprietary charging methods/signatures, all the methods are typically meant for stand-alone chargers. At least for QC ver.2 this TI document implies that if D+ doesn't hold its special value on device side, the power interface drops down to default 5-V level. So you can't maintain QC and free D+/D- for data communication. How things are with Qc v3.0 and v.4.0 is unclear.
However, if a host port supports USB 3.0+ communication, methods other than BC can be implemented, since USB 2.0 communication is secondary to USB 3.0 connection. Same goes for Type-C connector standard, which is/was quite open to possibility to have proprietary charging signatures even when Type-C has its own means to advertise its basic charging capability (at 5V level).